Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 338130.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.b1 | 338130b2 | \([1, -1, 0, -3172815, 2176073725]\) | \(986242575565963457/16426800\) | \(58833849063600\) | \([2]\) | \(5570560\) | \(2.1856\) | |
338130.b2 | 338130b1 | \([1, -1, 0, -198495, 33968461]\) | \(241490118740417/982575360\) | \(3519169310142720\) | \([2]\) | \(2785280\) | \(1.8390\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.b have rank \(2\).
Complex multiplication
The elliptic curves in class 338130.b do not have complex multiplication.Modular form 338130.2.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 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.