Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 257600.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.l1 | 257600l1 | \([0, 1, 0, -2248, -41742]\) | \(157114339136/181447\) | \(1451576000\) | \([2]\) | \(172032\) | \(0.67065\) | \(\Gamma_0(N)\)-optimal |
257600.l2 | 257600l2 | \([0, 1, 0, -1673, -63017]\) | \(-1012048064/2705927\) | \(-1385434624000\) | \([2]\) | \(344064\) | \(1.0172\) |
Rank
sage: E.rank()
The elliptic curves in class 257600.l have rank \(0\).
Complex multiplication
The elliptic curves in class 257600.l do not have complex multiplication.Modular form 257600.2.a.l
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.