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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 344760.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.a1 | 344760a4 | \([0, -1, 0, -43027456, -108619870100]\) | \(891190736491222802/3729375\) | \(36866008707840000\) | \([2]\) | \(20643840\) | \(2.8103\) | |
| 344760.a2 | 344760a2 | \([0, -1, 0, -2690536, -1694762564]\) | \(435792975088324/890127225\) | \(4399589479193625600\) | \([2, 2]\) | \(10321920\) | \(2.4638\) | |
| 344760.a3 | 344760a3 | \([0, -1, 0, -1777936, -2863255604]\) | \(-62875617222962/322034842935\) | \(-3183412588937716561920\) | \([2]\) | \(20643840\) | \(2.8103\) | |
| 344760.a4 | 344760a1 | \([0, -1, 0, -226516, -6416060]\) | \(1040212820176/587242305\) | \(725633649396414720\) | \([2]\) | \(5160960\) | \(2.1172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.a have rank \(2\).
Complex multiplication
The elliptic curves in class 344760.a do not have complex multiplication.Modular form 344760.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
