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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 75504.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75504.cq1 | 75504cm4 | \([0, 1, 0, -40151712, 97914005748]\) | \(986551739719628473/111045168\) | \(805778591200247808\) | \([2]\) | \(4915200\) | \(2.8602\) | |
| 75504.cq2 | 75504cm3 | \([0, 1, 0, -4529312, -1259870988]\) | \(1416134368422073/725251155408\) | \(5262650008067079733248\) | \([2]\) | \(4915200\) | \(2.8602\) | |
| 75504.cq3 | 75504cm2 | \([0, 1, 0, -2515872, 1521092340]\) | \(242702053576633/2554695936\) | \(18537675518263689216\) | \([2, 2]\) | \(2457600\) | \(2.5136\) | |
| 75504.cq4 | 75504cm1 | \([0, 1, 0, -37792, 59025140]\) | \(-822656953/207028224\) | \(-1502261770394271744\) | \([2]\) | \(1228800\) | \(2.1670\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75504.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 75504.cq do not have complex multiplication.Modular form 75504.2.a.cq
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.
