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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2925g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2925.d6 | 2925g1 | \([1, -1, 1, -24755, -1492878]\) | \(147281603041/5265\) | \(59971640625\) | \([2]\) | \(4608\) | \(1.1571\) | \(\Gamma_0(N)\)-optimal |
| 2925.d5 | 2925g2 | \([1, -1, 1, -25880, -1348878]\) | \(168288035761/27720225\) | \(315750687890625\) | \([2, 2]\) | \(9216\) | \(1.5037\) | |
| 2925.d4 | 2925g3 | \([1, -1, 1, -117005, 14142372]\) | \(15551989015681/1445900625\) | \(16469711806640625\) | \([2, 2]\) | \(18432\) | \(1.8503\) | |
| 2925.d7 | 2925g4 | \([1, -1, 1, 47245, -7637628]\) | \(1023887723039/2798036865\) | \(-31871388665390625\) | \([2]\) | \(18432\) | \(1.8503\) | |
| 2925.d2 | 2925g5 | \([1, -1, 1, -1828130, 951838872]\) | \(59319456301170001/594140625\) | \(6767633056640625\) | \([2, 2]\) | \(36864\) | \(2.1969\) | |
| 2925.d8 | 2925g6 | \([1, -1, 1, 136120, 66792372]\) | \(24487529386319/183539412225\) | \(-2090628617375390625\) | \([2]\) | \(36864\) | \(2.1969\) | |
| 2925.d1 | 2925g7 | \([1, -1, 1, -29250005, 60896057622]\) | \(242970740812818720001/24375\) | \(277646484375\) | \([2]\) | \(73728\) | \(2.5434\) | |
| 2925.d3 | 2925g8 | \([1, -1, 1, -1784255, 999662622]\) | \(-55150149867714721/5950927734375\) | \(-67784786224365234375\) | \([2]\) | \(73728\) | \(2.5434\) |
Rank
sage: E.rank()
The elliptic curves in class 2925g have rank \(0\).
Complex multiplication
The elliptic curves in class 2925g do not have complex multiplication.Modular form 2925.2.a.g
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 Cremona numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
