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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 62400.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.eu1 | 62400ck2 | \([0, 1, 0, -290233, -60261337]\) | \(42246001231552/14414517\) | \(922529088000000\) | \([2]\) | \(393216\) | \(1.8431\) | |
| 62400.eu2 | 62400ck1 | \([0, 1, 0, -15608, -1216962]\) | \(-420526439488/390971529\) | \(-390971529000000\) | \([2]\) | \(196608\) | \(1.4965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.eu do not have complex multiplication.Modular form 62400.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
