Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 24384bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24384.bj2 | 24384bi1 | \([0, 1, 0, -6524545, -6356293249]\) | \(117174888570509216929/1273887851544576\) | \(333942056955301330944\) | \([]\) | \(709632\) | \(2.7532\) | \(\Gamma_0(N)\)-optimal |
24384.bj1 | 24384bi2 | \([0, 1, 0, -1431110785, 20837616542591]\) | \(1236526859255318155975783969/38367061931916216\) | \(10057695083080244527104\) | \([]\) | \(4967424\) | \(3.7262\) |
Rank
sage: E.rank()
The elliptic curves in class 24384bi have rank \(1\).
Complex multiplication
The elliptic curves in class 24384bi do not have complex multiplication.Modular form 24384.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.