Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3630g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3630.i1 | 3630g1 | \([1, 0, 1, -1402514, -623939164]\) | \(129392980254539/3583180800\) | \(8448952893795532800\) | \([2]\) | \(118272\) | \(2.4112\) | \(\Gamma_0(N)\)-optimal |
3630.i2 | 3630g2 | \([1, 0, 1, 301166, -2042763868]\) | \(1281177907381/765275040000\) | \(-1804478513547932640000\) | \([2]\) | \(236544\) | \(2.7578\) |
Rank
sage: E.rank()
The elliptic curves in class 3630g have rank \(0\).
Complex multiplication
The elliptic curves in class 3630g do not have complex multiplication.Modular form 3630.2.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 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.