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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 11088.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.b1 | 11088bj1 | \([0, 0, 0, -12864, 561584]\) | \(-78843215872/539\) | \(-1609445376\) | \([]\) | \(14400\) | \(0.94745\) | \(\Gamma_0(N)\)-optimal |
| 11088.b2 | 11088bj2 | \([0, 0, 0, -7104, 1065584]\) | \(-13278380032/156590819\) | \(-467577680080896\) | \([]\) | \(43200\) | \(1.4968\) | |
| 11088.b3 | 11088bj3 | \([0, 0, 0, 63456, -27581776]\) | \(9463555063808/115539436859\) | \(-344998909829984256\) | \([]\) | \(129600\) | \(2.0461\) |
Rank
sage: E.rank()
The elliptic curves in class 11088.b have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.b do not have complex multiplication.Modular form 11088.2.a.b
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 LMFDB 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 LMFDB labels.
