Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 162240bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.gb4 | 162240bv1 | \([0, 1, 0, -3120641, -3506445825]\) | \(-2656166199049/2658140160\) | \(-3363395298276000399360\) | \([2]\) | \(10321920\) | \(2.8263\) | \(\Gamma_0(N)\)-optimal |
| 162240.gb3 | 162240bv2 | \([0, 1, 0, -58498561, -172176514561]\) | \(17496824387403529/6580454400\) | \(8326374102665684582400\) | \([2, 2]\) | \(20643840\) | \(3.1729\) | |
| 162240.gb2 | 162240bv3 | \([0, 1, 0, -67151361, -117900961281]\) | \(26465989780414729/10571870144160\) | \(13376788354475697226383360\) | \([2]\) | \(41287680\) | \(3.5195\) | |
| 162240.gb1 | 162240bv4 | \([0, 1, 0, -935892481, -11020450420225]\) | \(71647584155243142409/10140000\) | \(12830334847549440000\) | \([2]\) | \(41287680\) | \(3.5195\) |
Rank
sage: E.rank()
The elliptic curves in class 162240bv have rank \(1\).
Complex multiplication
The elliptic curves in class 162240bv do not have complex multiplication.Modular form 162240.2.a.bv
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.
