Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 141120.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.cj1 | 141120pf2 | \([0, 0, 0, -50639148, 138699700272]\) | \(68971442301/400\) | \(83286299412371865600\) | \([2]\) | \(8257536\) | \(3.0126\) | |
| 141120.cj2 | 141120pf1 | \([0, 0, 0, -3222828, 2083799088]\) | \(17779581/1280\) | \(266516158119589969920\) | \([2]\) | \(4128768\) | \(2.6660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.cj do not have complex multiplication.Modular form 141120.2.a.cj
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.
