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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 137904.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.s1 | 137904bl2 | \([0, -1, 0, -782188, -266004116]\) | \(42830942866000/146523\) | \(181053064987392\) | \([2]\) | \(1290240\) | \(1.9563\) | |
| 137904.s2 | 137904bl1 | \([0, -1, 0, -49573, -4020992]\) | \(174456832000/9771957\) | \(754677919923408\) | \([2]\) | \(645120\) | \(1.6097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 137904.s have rank \(1\).
Complex multiplication
The elliptic curves in class 137904.s do not have complex multiplication.Modular form 137904.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
