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SageMath
E = EllipticCurve("wv1")
E.isogeny_class()
Elliptic curves in class 369600wv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.wv4 | 369600wv1 | \([0, 1, 0, 5567, 99263]\) | \(4657463/3696\) | \(-15138816000000\) | \([2]\) | \(786432\) | \(1.2170\) | \(\Gamma_0(N)\)-optimal |
| 369600.wv3 | 369600wv2 | \([0, 1, 0, -26433, 835263]\) | \(498677257/213444\) | \(874266624000000\) | \([2, 2]\) | \(1572864\) | \(1.5635\) | |
| 369600.wv1 | 369600wv3 | \([0, 1, 0, -362433, 83827263]\) | \(1285429208617/614922\) | \(2518720512000000\) | \([2]\) | \(3145728\) | \(1.9101\) | |
| 369600.wv2 | 369600wv4 | \([0, 1, 0, -202433, -34540737]\) | \(223980311017/4278582\) | \(17525071872000000\) | \([2]\) | \(3145728\) | \(1.9101\) |
Rank
sage: E.rank()
The elliptic curves in class 369600wv have rank \(1\).
Complex multiplication
The elliptic curves in class 369600wv do not have complex multiplication.Modular form 369600.2.a.wv
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.
