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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 57960n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.e1 | 57960n1 | \([0, 0, 0, -423, -3078]\) | \(44851536/4025\) | \(751161600\) | \([2]\) | \(20480\) | \(0.44280\) | \(\Gamma_0(N)\)-optimal |
| 57960.e2 | 57960n2 | \([0, 0, 0, 477, -14418]\) | \(16078716/129605\) | \(-96749614080\) | \([2]\) | \(40960\) | \(0.78937\) |
Rank
sage: E.rank()
The elliptic curves in class 57960n have rank \(1\).
Complex multiplication
The elliptic curves in class 57960n do not have complex multiplication.Modular form 57960.2.a.n
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.
