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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 115920dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.ch4 | 115920dv1 | \([0, 0, 0, -490918683, -3650254584118]\) | \(4381924769947287308715481/608122186185572352000\) | \(1815843117995140073914368000\) | \([2]\) | \(61931520\) | \(3.9570\) | \(\Gamma_0(N)\)-optimal |
| 115920.ch2 | 115920dv2 | \([0, 0, 0, -7571755803, -253591059413302]\) | \(16077778198622525072705635801/388799208512064000000\) | \(1160948215829686910976000000\) | \([2, 2]\) | \(123863040\) | \(4.3036\) | |
| 115920.ch3 | 115920dv3 | \([0, 0, 0, -7289515803, -273368011349302]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-7493419040663248058480099328000\) | \([2]\) | \(247726080\) | \(4.6502\) | |
| 115920.ch1 | 115920dv4 | \([0, 0, 0, -121147389723, -16230025616545078]\) | \(65853432878493908038433301506521/38511703125000000\) | \(114995329344000000000000\) | \([2]\) | \(247726080\) | \(4.6502\) |
Rank
sage: E.rank()
The elliptic curves in class 115920dv have rank \(1\).
Complex multiplication
The elliptic curves in class 115920dv do not have complex multiplication.Modular form 115920.2.a.dv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
