Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 67760.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67760.v1 | 67760a2 | \([0, 0, 0, -3443, 60258]\) | \(3311744076/765625\) | \(1043504000000\) | \([2]\) | \(92160\) | \(1.0183\) | |
67760.v2 | 67760a1 | \([0, 0, 0, -3223, 70422]\) | \(10866423024/875\) | \(298144000\) | \([2]\) | \(46080\) | \(0.67173\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67760.v have rank \(1\).
Complex multiplication
The elliptic curves in class 67760.v do not have complex multiplication.Modular form 67760.2.a.v
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.