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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 97020.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.d1 | 97020f3 | \([0, 0, 0, -2931768, 1932150213]\) | \(75216478666752/326095\) | \(12082134194277840\) | \([2]\) | \(1492992\) | \(2.2927\) | |
| 97020.d2 | 97020f4 | \([0, 0, 0, -2885463, 1996134462]\) | \(-4481782160112/310023175\) | \(-183786521286672057600\) | \([2]\) | \(2985984\) | \(2.6393\) | |
| 97020.d3 | 97020f1 | \([0, 0, 0, -50568, 353633]\) | \(281370820608/161767375\) | \(8221724597394000\) | \([2]\) | \(497664\) | \(1.7434\) | \(\Gamma_0(N)\)-optimal |
| 97020.d4 | 97020f2 | \([0, 0, 0, 201537, 2824262]\) | \(1113258734352/648484375\) | \(-527340936276000000\) | \([2]\) | \(995328\) | \(2.0900\) |
Rank
sage: E.rank()
The elliptic curves in class 97020.d have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.d do not have complex multiplication.Modular form 97020.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
