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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 54978.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54978.p1 | 54978z2 | \([1, 0, 1, -146242, 21458420]\) | \(2940001530995593/8673562656\) | \(1020435972915744\) | \([2]\) | \(345600\) | \(1.7499\) | |
| 54978.p2 | 54978z1 | \([1, 0, 1, -12962, 26996]\) | \(2046931732873/1181672448\) | \(139022581834752\) | \([2]\) | \(172800\) | \(1.4033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54978.p have rank \(0\).
Complex multiplication
The elliptic curves in class 54978.p do not have complex multiplication.Modular form 54978.2.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.
