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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 65025bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65025.z2 | 65025bi1 | \([0, 0, 1, 43350, 16734906]\) | \(32768/459\) | \(-126198376572796875\) | \([]\) | \(497664\) | \(1.9621\) | \(\Gamma_0(N)\)-optimal |
| 65025.z1 | 65025bi2 | \([0, 0, 1, -3858150, 2918475531]\) | \(-23100424192/14739\) | \(-4052370092170921875\) | \([]\) | \(1492992\) | \(2.5114\) |
Rank
sage: E.rank()
The elliptic curves in class 65025bi have rank \(2\).
Complex multiplication
The elliptic curves in class 65025bi do not have complex multiplication.Modular form 65025.2.a.bi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
