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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2760d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2760.a3 | 2760d1 | \([0, -1, 0, -116, -444]\) | \(680136784/345\) | \(88320\) | \([2]\) | \(384\) | \(-0.098917\) | \(\Gamma_0(N)\)-optimal |
| 2760.a2 | 2760d2 | \([0, -1, 0, -136, -260]\) | \(273671716/119025\) | \(121881600\) | \([2, 2]\) | \(768\) | \(0.24766\) | |
| 2760.a1 | 2760d3 | \([0, -1, 0, -1056, 13356]\) | \(63649751618/1164375\) | \(2384640000\) | \([2]\) | \(1536\) | \(0.59423\) | |
| 2760.a4 | 2760d4 | \([0, -1, 0, 464, -2420]\) | \(5382838942/4197615\) | \(-8596715520\) | \([2]\) | \(1536\) | \(0.59423\) |
Rank
sage: E.rank()
The elliptic curves in class 2760d have rank \(0\).
Complex multiplication
The elliptic curves in class 2760d do not have complex multiplication.Modular form 2760.2.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 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.
