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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 179520.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.c1 | 179520dj3 | \([0, -1, 0, -16683041, -8179557759]\) | \(15671099011706354272328/8185672760009765625\) | \(268228125000000000000000\) | \([2]\) | \(28508160\) | \(3.1873\) | |
| 179520.c2 | 179520dj2 | \([0, -1, 0, -13249721, -18540630855]\) | \(62803521661592763722944/71946327041015625\) | \(294692155560000000000\) | \([2, 2]\) | \(14254080\) | \(2.8407\) | |
| 179520.c3 | 179520dj1 | \([0, -1, 0, -13246076, -18551355174]\) | \(4016109065546377048511296/5279534184375\) | \(337890187800000\) | \([2]\) | \(7127040\) | \(2.4942\) | \(\Gamma_0(N)\)-optimal |
| 179520.c4 | 179520dj4 | \([0, -1, 0, -9874721, -28215405855]\) | \(-3249737806881412215368/8617392958529334375\) | \(-282374732465089228800000\) | \([2]\) | \(28508160\) | \(3.1873\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.c have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.c do not have complex multiplication.Modular form 179520.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
