Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 151725cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151725.cj4 | 151725cv1 | \([1, 1, 0, -1307875, -1308875000]\) | \(-656008386769/1581036975\) | \(-596287329306465234375\) | \([2]\) | \(5308416\) | \(2.6746\) | \(\Gamma_0(N)\)-optimal |
| 151725.cj3 | 151725cv2 | \([1, 1, 0, -27643000, -55901589125]\) | \(6193921595708449/6452105625\) | \(2433408511230087890625\) | \([2, 2]\) | \(10616832\) | \(3.0211\) | |
| 151725.cj2 | 151725cv3 | \([1, 1, 0, -34470625, -26180937500]\) | \(12010404962647729/6166198828125\) | \(2325578901274786376953125\) | \([2]\) | \(21233664\) | \(3.3677\) | |
| 151725.cj1 | 151725cv4 | \([1, 1, 0, -442177375, -3579029242250]\) | \(25351269426118370449/27551475\) | \(10391025451004296875\) | \([2]\) | \(21233664\) | \(3.3677\) |
Rank
sage: E.rank()
The elliptic curves in class 151725cv have rank \(0\).
Complex multiplication
The elliptic curves in class 151725cv do not have complex multiplication.Modular form 151725.2.a.cv
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.
