Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10480.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10480.j1 | 10480k1 | \([0, 1, 0, -1520, -25900]\) | \(-94881210481/13100000\) | \(-53657600000\) | \([]\) | \(6240\) | \(0.79054\) | \(\Gamma_0(N)\)-optimal |
| 10480.j2 | 10480k2 | \([0, 1, 0, -720, 1912340]\) | \(-10091699281/385794896510\) | \(-1580215896104960\) | \([]\) | \(31200\) | \(1.5953\) |
Rank
sage: E.rank()
The elliptic curves in class 10480.j have rank \(1\).
Complex multiplication
The elliptic curves in class 10480.j do not have complex multiplication.Modular form 10480.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
