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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2760.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2760.d1 | 2760a3 | \([0, -1, 0, -2456, 47676]\) | \(1600610497636/9315\) | \(9538560\) | \([2]\) | \(1792\) | \(0.52925\) | |
2760.d2 | 2760a2 | \([0, -1, 0, -156, 756]\) | \(1650587344/119025\) | \(30470400\) | \([2, 2]\) | \(896\) | \(0.18267\) | |
2760.d3 | 2760a1 | \([0, -1, 0, -31, -44]\) | \(212629504/43125\) | \(690000\) | \([2]\) | \(448\) | \(-0.16390\) | \(\Gamma_0(N)\)-optimal |
2760.d4 | 2760a4 | \([0, -1, 0, 144, 3036]\) | \(320251964/4197615\) | \(-4298357760\) | \([2]\) | \(1792\) | \(0.52925\) |
Rank
sage: E.rank()
The elliptic curves in class 2760.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2760.d 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 LMFDB 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 LMFDB labels.