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SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 374850.iq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374850.iq1 | 374850iq8 | \([1, -1, 1, -1251006980, -17030508402603]\) | \(161572377633716256481/914742821250\) | \(1225842867050138613281250\) | \([2]\) | \(150994944\) | \(3.8137\) | |
| 374850.iq2 | 374850iq3 | \([1, -1, 1, -239904230, 1430286971397]\) | \(1139466686381936641/4080\) | \(5467590213750000\) | \([2]\) | \(37748736\) | \(3.1206\) | |
| 374850.iq3 | 374850iq6 | \([1, -1, 1, -79600730, -255970902603]\) | \(41623544884956481/2962701562500\) | \(3970303448379125976562500\) | \([2, 2]\) | \(75497472\) | \(3.4671\) | |
| 374850.iq4 | 374850iq4 | \([1, -1, 1, -15876230, 19573835397]\) | \(330240275458561/67652010000\) | \(90660163680518906250000\) | \([2, 2]\) | \(37748736\) | \(3.1206\) | |
| 374850.iq5 | 374850iq2 | \([1, -1, 1, -14994230, 22350371397]\) | \(278202094583041/16646400\) | \(22307768072100000000\) | \([2, 2]\) | \(18874368\) | \(2.7740\) | |
| 374850.iq6 | 374850iq1 | \([1, -1, 1, -882230, 392099397]\) | \(-56667352321/16711680\) | \(-22395249515520000000\) | \([2]\) | \(9437184\) | \(2.4274\) | \(\Gamma_0(N)\)-optimal |
| 374850.iq7 | 374850iq5 | \([1, -1, 1, 33736270, 117409685397]\) | \(3168685387909439/6278181696900\) | \(-8413363923067355076562500\) | \([2]\) | \(75497472\) | \(3.4671\) | |
| 374850.iq8 | 374850iq7 | \([1, -1, 1, 72213520, -1117061328603]\) | \(31077313442863199/420227050781250\) | \(-563144438824653625488281250\) | \([2]\) | \(150994944\) | \(3.8137\) |
Rank
sage: E.rank()
The elliptic curves in class 374850.iq have rank \(2\).
Complex multiplication
The elliptic curves in class 374850.iq do not have complex multiplication.Modular form 374850.2.a.iq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
