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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 11376r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11376.p2 | 11376r1 | \([0, 0, 0, 141, 1330]\) | \(103823/316\) | \(-943570944\) | \([2]\) | \(3456\) | \(0.40541\) | \(\Gamma_0(N)\)-optimal |
| 11376.p1 | 11376r2 | \([0, 0, 0, -1299, 15442]\) | \(81182737/12482\) | \(37271052288\) | \([2]\) | \(6912\) | \(0.75199\) |
Rank
sage: E.rank()
The elliptic curves in class 11376r have rank \(0\).
Complex multiplication
The elliptic curves in class 11376r do not have complex multiplication.Modular form 11376.2.a.r
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.
