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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 139230dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139230.d3 | 139230dv1 | \([1, -1, 0, -11602500, -12150639280]\) | \(236946848159403385640001/49591036552580956160\) | \(36151865646831517040640\) | \([2]\) | \(11141120\) | \(3.0434\) | \(\Gamma_0(N)\)-optimal |
| 139230.d2 | 139230dv2 | \([1, -1, 0, -58788420, 162805314896]\) | \(30822761984985495827731521/2133077487524223385600\) | \(1555013488405158848102400\) | \([2, 2]\) | \(22282240\) | \(3.3899\) | |
| 139230.d1 | 139230dv3 | \([1, -1, 0, -924401220, 10817979515216]\) | \(119833353753791357767404000321/639263335167953699840\) | \(466022971337438247183360\) | \([2]\) | \(44564480\) | \(3.7365\) | |
| 139230.d4 | 139230dv4 | \([1, -1, 0, 51849660, 704245950800]\) | \(21146277044499148416871359/306151868455702272640000\) | \(-223184712104206956754560000\) | \([2]\) | \(44564480\) | \(3.7365\) |
Rank
sage: E.rank()
The elliptic curves in class 139230dv have rank \(1\).
Complex multiplication
The elliptic curves in class 139230dv do not have complex multiplication.Modular form 139230.2.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.
