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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 83760n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83760.i1 | 83760n1 | \([0, -1, 0, -726960, -238478400]\) | \(-10372797669976737841/7632630000000\) | \(-31263252480000000\) | \([]\) | \(931392\) | \(2.0992\) | \(\Gamma_0(N)\)-optimal |
| 83760.i2 | 83760n2 | \([0, -1, 0, 2918640, 13254112320]\) | \(671282315177095816559/18919046447754148470\) | \(-77492414250000992133120\) | \([]\) | \(6519744\) | \(3.0721\) |
Rank
sage: E.rank()
The elliptic curves in class 83760n have rank \(1\).
Complex multiplication
The elliptic curves in class 83760n do not have complex multiplication.Modular form 83760.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
