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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 136290.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 136290.ct1 | 136290a4 | \([1, 0, 0, -53380863340, -4747083934971658]\) | \(16822110927907071112393084202410196161/525702416105845179466650\) | \(525702416105845179466650\) | \([2]\) | \(323200000\) | \(4.5055\) | |
| 136290.ct2 | 136290a3 | \([1, 0, 0, -3336162410, -74180003513280]\) | \(-4106437962229085333075261665806241/726025922559946496763017820\) | \(-726025922559946496763017820\) | \([2]\) | \(161600000\) | \(4.1589\) | |
| 136290.ct3 | 136290a2 | \([1, 0, 0, -126947590, 21290730692]\) | \(226254431386145697240615608161/130738259239901991562500000\) | \(130738259239901991562500000\) | \([10]\) | \(64640000\) | \(3.7008\) | |
| 136290.ct4 | 136290a1 | \([1, 0, 0, 31710490, 2664272100]\) | \(3526408097252790554911347359/2043805832116142371200000\) | \(-2043805832116142371200000\) | \([10]\) | \(32320000\) | \(3.3542\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 136290.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 136290.ct do not have complex multiplication.Modular form 136290.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
