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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 371280fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.fv4 | 371280fv1 | \([0, 1, 0, -86840, 32340]\) | \(17681870665400761/10232167895040\) | \(41910959698083840\) | \([2]\) | \(2654208\) | \(1.8790\) | \(\Gamma_0(N)\)-optimal |
| 371280.fv2 | 371280fv2 | \([0, 1, 0, -952120, -356809132]\) | \(23304472877725373881/82743765249600\) | \(338918462462361600\) | \([2, 2]\) | \(5308416\) | \(2.2256\) | |
| 371280.fv3 | 371280fv3 | \([0, 1, 0, -527800, -676067500]\) | \(-3969837635175430201/45883867071315000\) | \(-187940319524106240000\) | \([2]\) | \(10616832\) | \(2.5721\) | |
| 371280.fv1 | 371280fv4 | \([0, 1, 0, -15220920, -22861560492]\) | \(95210863233510962017081/1206641250360\) | \(4942402561474560\) | \([2]\) | \(10616832\) | \(2.5721\) |
Rank
sage: E.rank()
The elliptic curves in class 371280fv have rank \(0\).
Complex multiplication
The elliptic curves in class 371280fv do not have complex multiplication.Modular form 371280.2.a.fv
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.
