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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 157050.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 157050.v1 | 157050k1 | \([1, -1, 1, -10222880, -12586232253]\) | \(-10372797669976737841/7632630000000\) | \(-86940426093750000000\) | \([]\) | \(7451136\) | \(2.7600\) | \(\Gamma_0(N)\)-optimal |
| 157050.v2 | 157050k2 | \([1, -1, 1, 41043370, 698988372747]\) | \(671282315177095816559/18919046447754148470\) | \(-215499763443949597416093750\) | \([]\) | \(52157952\) | \(3.7330\) |
Rank
sage: E.rank()
The elliptic curves in class 157050.v have rank \(1\).
Complex multiplication
The elliptic curves in class 157050.v do not have complex multiplication.Modular form 157050.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
