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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 20400.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20400.c1 | 20400o1 | \([0, -1, 0, -203583, -35284338]\) | \(29860725364736/3581577\) | \(111924281250000\) | \([2]\) | \(149760\) | \(1.7205\) | \(\Gamma_0(N)\)-optimal |
| 20400.c2 | 20400o2 | \([0, -1, 0, -186708, -41393088]\) | \(-1439609866256/651714363\) | \(-325857181500000000\) | \([2]\) | \(299520\) | \(2.0671\) |
Rank
sage: E.rank()
The elliptic curves in class 20400.c have rank \(0\).
Complex multiplication
The elliptic curves in class 20400.c do not have complex multiplication.Modular form 20400.2.a.c
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.
