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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4368.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.c1 | 4368s2 | \([0, -1, 0, -404, -2436]\) | \(28556329552/5373459\) | \(1375605504\) | \([2]\) | \(1920\) | \(0.47132\) | |
| 4368.c2 | 4368s1 | \([0, -1, 0, 51, -252]\) | \(899022848/2012283\) | \(-32196528\) | \([2]\) | \(960\) | \(0.12475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4368.c have rank \(1\).
Complex multiplication
The elliptic curves in class 4368.c do not have complex multiplication.Modular form 4368.2.a.c
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.
