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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2790.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2790.c1 | 2790g5 | \([1, -1, 0, -2767680, 1772929620]\) | \(3216206300355197383681/57660\) | \(42034140\) | \([2]\) | \(32768\) | \(1.9311\) | |
| 2790.c2 | 2790g4 | \([1, -1, 0, -172980, 27734400]\) | \(785209010066844481/3324675600\) | \(2423688512400\) | \([2, 2]\) | \(16384\) | \(1.5846\) | |
| 2790.c3 | 2790g6 | \([1, -1, 0, -170280, 28639980]\) | \(-749011598724977281/51173462246460\) | \(-37305453977669340\) | \([2]\) | \(32768\) | \(1.9311\) | |
| 2790.c4 | 2790g3 | \([1, -1, 0, -33300, -1815264]\) | \(5601911201812801/1271193750000\) | \(926700243750000\) | \([2]\) | \(16384\) | \(1.5846\) | |
| 2790.c5 | 2790g2 | \([1, -1, 0, -10980, 421200]\) | \(200828550012481/12454560000\) | \(9079374240000\) | \([2, 2]\) | \(8192\) | \(1.2380\) | |
| 2790.c6 | 2790g1 | \([1, -1, 0, 540, 27216]\) | \(23862997439/457113600\) | \(-333235814400\) | \([2]\) | \(4096\) | \(0.89141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.c do not have complex multiplication.Modular form 2790.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
