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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 254016dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254016.dv3 | 254016dv1 | \([0, 0, 0, -14700, 718928]\) | \(-140625/8\) | \(-19984954687488\) | \([]\) | \(414720\) | \(1.3091\) | \(\Gamma_0(N)\)-optimal |
| 254016.dv4 | 254016dv2 | \([0, 0, 0, 79380, 1333584]\) | \(3375/2\) | \(-32780321926152192\) | \([]\) | \(1244160\) | \(1.8584\) | |
| 254016.dv2 | 254016dv3 | \([0, 0, 0, -296940, -126514864]\) | \(-1159088625/2097152\) | \(-5238935961596854272\) | \([]\) | \(2903040\) | \(2.2820\) | |
| 254016.dv1 | 254016dv4 | \([0, 0, 0, -30402540, -64522794672]\) | \(-189613868625/128\) | \(-2097940603273740288\) | \([]\) | \(8709120\) | \(2.8313\) |
Rank
sage: E.rank()
The elliptic curves in class 254016dv have rank \(1\).
Complex multiplication
The elliptic curves in class 254016dv do not have complex multiplication.Modular form 254016.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
