Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 86240.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86240.g1 | 86240bo2 | \([0, 1, 0, -207041, 34499695]\) | \(2036792051776/107421875\) | \(51765560000000000\) | \([2]\) | \(737280\) | \(1.9641\) | |
86240.g2 | 86240bo1 | \([0, 1, 0, -204346, 35486604]\) | \(125330290485184/378125\) | \(2847105800000\) | \([2]\) | \(368640\) | \(1.6175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86240.g have rank \(0\).
Complex multiplication
The elliptic curves in class 86240.g do not have complex multiplication.Modular form 86240.2.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.