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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 23520.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.d1 | 23520d4 | \([0, -1, 0, -33336, -2330460]\) | \(68017239368/39375\) | \(2371803840000\) | \([2]\) | \(49152\) | \(1.3201\) | |
| 23520.d2 | 23520d3 | \([0, -1, 0, -19616, 1048776]\) | \(13858588808/229635\) | \(13832359994880\) | \([2]\) | \(49152\) | \(1.3201\) | |
| 23520.d3 | 23520d1 | \([0, -1, 0, -2466, -21384]\) | \(220348864/99225\) | \(747118209600\) | \([2, 2]\) | \(24576\) | \(0.97357\) | \(\Gamma_0(N)\)-optimal |
| 23520.d4 | 23520d2 | \([0, -1, 0, 8559, -169119]\) | \(143877824/108045\) | \(-52065837895680\) | \([2]\) | \(49152\) | \(1.3201\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.d have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.d do not have complex multiplication.Modular form 23520.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
