Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 49686d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.n2 | 49686d1 | \([1, 1, 0, 10, -762]\) | \(1625/4374\) | \(-253547658\) | \([]\) | \(18816\) | \(0.29154\) | \(\Gamma_0(N)\)-optimal |
49686.n1 | 49686d2 | \([1, 1, 0, -21830, 1234836]\) | \(-168712375/384\) | \(-2618787679872\) | \([]\) | \(131712\) | \(1.2645\) |
Rank
sage: E.rank()
The elliptic curves in class 49686d have rank \(0\).
Complex multiplication
The elliptic curves in class 49686d do not have complex multiplication.Modular form 49686.2.a.d
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.