Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 458640.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.g1 | 458640g2 | \([0, 0, 0, -8071623, 8790522678]\) | \(98104024066032/462109375\) | \(273945567086100000000\) | \([2]\) | \(25952256\) | \(2.7713\) | \(\Gamma_0(N)\)-optimal* |
458640.g2 | 458640g1 | \([0, 0, 0, -246078, 277894827]\) | \(-44477724672/874680625\) | \(-32407760586285630000\) | \([2]\) | \(12976128\) | \(2.4247\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 458640.g have rank \(1\).
Complex multiplication
The elliptic curves in class 458640.g do not have complex multiplication.Modular form 458640.2.a.g
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 LMFDB 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 LMFDB labels.