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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 150696.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 150696.w1 | 150696q4 | \([0, 0, 0, -401859, -98052498]\) | \(9614292367656708/2093\) | \(1562416128\) | \([2]\) | \(524288\) | \(1.5885\) | |
| 150696.w2 | 150696q3 | \([0, 0, 0, -29259, -992682]\) | \(3710860803108/1577224103\) | \(1177391483993088\) | \([2]\) | \(524288\) | \(1.5885\) | |
| 150696.w3 | 150696q2 | \([0, 0, 0, -25119, -1531710]\) | \(9392111857872/4380649\) | \(817534238976\) | \([2, 2]\) | \(262144\) | \(1.2419\) | |
| 150696.w4 | 150696q1 | \([0, 0, 0, -1314, -31995]\) | \(-21511084032/25465531\) | \(-297029953584\) | \([2]\) | \(131072\) | \(0.89535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 150696.w have rank \(0\).
Complex multiplication
The elliptic curves in class 150696.w do not have complex multiplication.Modular form 150696.2.a.w
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
