Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 249090t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.t2 | 249090t1 | \([1, 1, 0, -88452, 10132176]\) | \(-1626794704081/8125440\) | \(-382268483312640\) | \([2]\) | \(1451520\) | \(1.6456\) | \(\Gamma_0(N)\)-optimal |
249090.t1 | 249090t2 | \([1, 1, 0, -1416932, 648599664]\) | \(6687281588245201/165600\) | \(7790797893600\) | \([2]\) | \(2903040\) | \(1.9921\) |
Rank
sage: E.rank()
The elliptic curves in class 249090t have rank \(1\).
Complex multiplication
The elliptic curves in class 249090t do not have complex multiplication.Modular form 249090.2.a.t
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.