Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 510.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
510.b1 | 510b2 | \([1, 0, 1, -11603, -482002]\) | \(172735174415217961/39657600\) | \(39657600\) | \([2]\) | \(672\) | \(0.83868\) | |
510.b2 | 510b1 | \([1, 0, 1, -723, -7634]\) | \(-41713327443241/639221760\) | \(-639221760\) | \([2]\) | \(336\) | \(0.49211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 510.b have rank \(0\).
Complex multiplication
The elliptic curves in class 510.b do not have complex multiplication.Modular form 510.2.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.