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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 57960j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.k2 | 57960j1 | \([0, 0, 0, -1083, 3782]\) | \(188183524/100625\) | \(75116160000\) | \([2]\) | \(55296\) | \(0.77813\) | \(\Gamma_0(N)\)-optimal |
| 57960.k1 | 57960j2 | \([0, 0, 0, -10083, -386818]\) | \(75933869762/648025\) | \(967496140800\) | \([2]\) | \(110592\) | \(1.1247\) |
Rank
sage: E.rank()
The elliptic curves in class 57960j have rank \(0\).
Complex multiplication
The elliptic curves in class 57960j do not have complex multiplication.Modular form 57960.2.a.j
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 Cremona 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 Cremona labels.
