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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 24990bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.bh2 | 24990bi1 | \([1, 0, 1, -82493, 23840408]\) | \(-527690404915129/1782829440000\) | \(-209748100786560000\) | \([2]\) | \(368640\) | \(2.0099\) | \(\Gamma_0(N)\)-optimal |
24990.bh1 | 24990bi2 | \([1, 0, 1, -1846493, 964405208]\) | \(5918043195362419129/8515734343200\) | \(1001867629743136800\) | \([2]\) | \(737280\) | \(2.3565\) |
Rank
sage: E.rank()
The elliptic curves in class 24990bi have rank \(1\).
Complex multiplication
The elliptic curves in class 24990bi do not have complex multiplication.Modular form 24990.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.