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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 11088cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.l2 | 11088cb1 | \([0, 0, 0, -2091, -38054]\) | \(-338608873/13552\) | \(-40466055168\) | \([2]\) | \(9216\) | \(0.80357\) | \(\Gamma_0(N)\)-optimal |
| 11088.l1 | 11088cb2 | \([0, 0, 0, -33771, -2388710]\) | \(1426487591593/2156\) | \(6437781504\) | \([2]\) | \(18432\) | \(1.1501\) |
Rank
sage: E.rank()
The elliptic curves in class 11088cb have rank \(1\).
Complex multiplication
The elliptic curves in class 11088cb do not have complex multiplication.Modular form 11088.2.a.cb
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.
