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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1260.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1260.d1 | 1260b4 | \([0, 0, 0, -18063, -934362]\) | \(129348709488/6125\) | \(30862944000\) | \([2]\) | \(1728\) | \(1.0866\) | |
| 1260.d2 | 1260b3 | \([0, 0, 0, -1188, -12987]\) | \(588791808/109375\) | \(34445250000\) | \([2]\) | \(864\) | \(0.74005\) | |
| 1260.d3 | 1260b2 | \([0, 0, 0, -423, 1342]\) | \(1210991472/588245\) | \(4065949440\) | \([6]\) | \(576\) | \(0.53732\) | |
| 1260.d4 | 1260b1 | \([0, 0, 0, -348, 2497]\) | \(10788913152/8575\) | \(3704400\) | \([6]\) | \(288\) | \(0.19075\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1260.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1260.d do not have complex multiplication.Modular form 1260.2.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.
