Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 130696b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130696.c2 | 130696b1 | \([0, 1, 0, -8008, 198144]\) | \(62500/17\) | \(15449664078848\) | \([2]\) | \(230400\) | \(1.2386\) | \(\Gamma_0(N)\)-optimal |
130696.c1 | 130696b2 | \([0, 1, 0, -46448, -3707360]\) | \(6097250/289\) | \(525288578680832\) | \([2]\) | \(460800\) | \(1.5851\) |
Rank
sage: E.rank()
The elliptic curves in class 130696b have rank \(0\).
Complex multiplication
The elliptic curves in class 130696b do not have complex multiplication.Modular form 130696.2.a.b
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.