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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 25168bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25168.g3 | 25168bb1 | \([0, -1, 0, 928, 17536]\) | \(12167/26\) | \(-188664160256\) | \([]\) | \(17280\) | \(0.84787\) | \(\Gamma_0(N)\)-optimal |
| 25168.g2 | 25168bb2 | \([0, -1, 0, -8752, -625216]\) | \(-10218313/17576\) | \(-127536972333056\) | \([]\) | \(51840\) | \(1.3972\) | |
| 25168.g1 | 25168bb3 | \([0, -1, 0, -889632, -322674944]\) | \(-10730978619193/6656\) | \(-48298025025536\) | \([]\) | \(155520\) | \(1.9465\) |
Rank
sage: E.rank()
The elliptic curves in class 25168bb have rank \(1\).
Complex multiplication
The elliptic curves in class 25168bb do not have complex multiplication.Modular form 25168.2.a.bb
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.
