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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 136710gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 136710.l2 | 136710gl1 | \([1, -1, 0, 27480, -663104]\) | \(722458663317/476656000\) | \(-1514108747088000\) | \([]\) | \(762048\) | \(1.6016\) | \(\Gamma_0(N)\)-optimal |
| 136710.l1 | 136710gl2 | \([1, -1, 0, -314295, 79714781]\) | \(-1482713947827/325058560\) | \(-752733318304235520\) | \([]\) | \(2286144\) | \(2.1509\) |
Rank
sage: E.rank()
The elliptic curves in class 136710gl have rank \(0\).
Complex multiplication
The elliptic curves in class 136710gl do not have complex multiplication.Modular form 136710.2.a.gl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
