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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 115920.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.f1 | 115920cd1 | \([0, 0, 0, -21843, 1059858]\) | \(14295828483/2254000\) | \(181721014272000\) | \([2]\) | \(331776\) | \(1.4589\) | \(\Gamma_0(N)\)-optimal |
| 115920.f2 | 115920cd2 | \([0, 0, 0, 38637, 5886162]\) | \(79119341757/231437500\) | \(-18658854144000000\) | \([2]\) | \(663552\) | \(1.8055\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.f have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.f do not have complex multiplication.Modular form 115920.2.a.f
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.
