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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 40362v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40362.y3 | 40362v1 | \([1, 1, 1, -40382, 3096299]\) | \(8205738913/31248\) | \(27732715023888\) | \([4]\) | \(122880\) | \(1.4383\) | \(\Gamma_0(N)\)-optimal |
| 40362.y2 | 40362v2 | \([1, 1, 1, -59602, -178789]\) | \(26383748833/15256836\) | \(13540498110413316\) | \([2, 2]\) | \(245760\) | \(1.7849\) | |
| 40362.y4 | 40362v3 | \([1, 1, 1, 238308, -1132101]\) | \(1686433811327/976683582\) | \(-866810274197265342\) | \([2]\) | \(491520\) | \(2.1314\) | |
| 40362.y1 | 40362v4 | \([1, 1, 1, -665032, -208446709]\) | \(36650611029313/116363646\) | \(103273164159580926\) | \([2]\) | \(491520\) | \(2.1314\) |
Rank
sage: E.rank()
The elliptic curves in class 40362v have rank \(1\).
Complex multiplication
The elliptic curves in class 40362v do not have complex multiplication.Modular form 40362.2.a.v
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 Cremona 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 Cremona labels.
