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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 112632l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112632.bb1 | 112632l1 | \([0, 1, 0, -235131, -41307318]\) | \(1909913257984/129730653\) | \(97652685809444688\) | \([2]\) | \(1451520\) | \(2.0086\) | \(\Gamma_0(N)\)-optimal |
| 112632.bb2 | 112632l2 | \([0, 1, 0, 203484, -177277968]\) | \(77366117936/1172914587\) | \(-14126284821290533632\) | \([2]\) | \(2903040\) | \(2.3552\) |
Rank
sage: E.rank()
The elliptic curves in class 112632l have rank \(0\).
Complex multiplication
The elliptic curves in class 112632l do not have complex multiplication.Modular form 112632.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
