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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 15246.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15246.p1 | 15246o2 | \([1, -1, 0, -114912, -14242046]\) | \(129938649625/7072758\) | \(9134240409488502\) | \([2]\) | \(122880\) | \(1.8185\) | |
| 15246.p2 | 15246o1 | \([1, -1, 0, 4878, -897440]\) | \(9938375/274428\) | \(-354414971796732\) | \([2]\) | \(61440\) | \(1.4719\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15246.p have rank \(0\).
Complex multiplication
The elliptic curves in class 15246.p do not have complex multiplication.Modular form 15246.2.a.p
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.
