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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 53040.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.cj1 | 53040cz4 | \([0, 1, 0, -1225920, -521965260]\) | \(49745123032831462081/97939634471640\) | \(401160742795837440\) | \([2]\) | \(1105920\) | \(2.2658\) | |
| 53040.cj2 | 53040cz3 | \([0, 1, 0, -1027520, 398475060]\) | \(29291056630578924481/175463302795560\) | \(718697688250613760\) | \([4]\) | \(1105920\) | \(2.2658\) | |
| 53040.cj3 | 53040cz2 | \([0, 1, 0, -102720, -2148300]\) | \(29263955267177281/16463793153600\) | \(67435696757145600\) | \([2, 2]\) | \(552960\) | \(1.9193\) | |
| 53040.cj4 | 53040cz1 | \([0, 1, 0, 25280, -253900]\) | \(436192097814719/259683840000\) | \(-1063665008640000\) | \([2]\) | \(276480\) | \(1.5727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53040.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 53040.cj do not have complex multiplication.Modular form 53040.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
