Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 15680.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.x1 | 15680ds2 | \([0, 1, 0, -47105, 2782975]\) | \(2185454/625\) | \(3305767485440000\) | \([2]\) | \(86016\) | \(1.6844\) | |
15680.x2 | 15680ds1 | \([0, 1, 0, 7775, 291423]\) | \(19652/25\) | \(-66115349708800\) | \([2]\) | \(43008\) | \(1.3379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.x have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.x do not have complex multiplication.Modular form 15680.2.a.x
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.