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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 38640.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.n1 | 38640be2 | \([0, -1, 0, -379541, 91405305]\) | \(-23618971583050153984/391556092921875\) | \(-100238359788000000\) | \([]\) | \(466560\) | \(2.0617\) | |
| 38640.n2 | 38640be1 | \([0, -1, 0, 17899, 600201]\) | \(2477112820760576/2053567248075\) | \(-525713215507200\) | \([]\) | \(155520\) | \(1.5124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.n have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.n do not have complex multiplication.Modular form 38640.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
