Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2520.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2520.e1 | 2520k2 | \([0, 0, 0, -2414583, 1444120218]\) | \(308971819397054448/6565234375\) | \(33081218100000000\) | \([2]\) | \(46080\) | \(2.2873\) | |
2520.e2 | 2520k1 | \([0, 0, 0, -145638, 24214437]\) | \(-1084767227025408/176547030625\) | \(-55599603260670000\) | \([2]\) | \(23040\) | \(1.9407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2520.e have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.e do not have complex multiplication.Modular form 2520.2.a.e
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.