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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11200c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11200.cg2 | 11200c1 | \([0, 1, 0, -133, 613]\) | \(-262144/35\) | \(-35000000\) | \([]\) | \(2304\) | \(0.18014\) | \(\Gamma_0(N)\)-optimal |
| 11200.cg3 | 11200c2 | \([0, 1, 0, 867, -1387]\) | \(71991296/42875\) | \(-42875000000\) | \([]\) | \(6912\) | \(0.72945\) | |
| 11200.cg1 | 11200c3 | \([0, 1, 0, -13133, -610387]\) | \(-250523582464/13671875\) | \(-13671875000000\) | \([]\) | \(20736\) | \(1.2788\) |
Rank
sage: E.rank()
The elliptic curves in class 11200c have rank \(1\).
Complex multiplication
The elliptic curves in class 11200c do not have complex multiplication.Modular form 11200.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
