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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 216384.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
216384.d1 | 216384gw2 | \([0, -1, 0, -227425, 10587361]\) | \(42180533641/22862322\) | \(705096403118456832\) | \([2]\) | \(3538944\) | \(2.1157\) | |
216384.d2 | 216384gw1 | \([0, -1, 0, 54815, 1273441]\) | \(590589719/365148\) | \(-11261521966399488\) | \([2]\) | \(1769472\) | \(1.7691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 216384.d have rank \(1\).
Complex multiplication
The elliptic curves in class 216384.d do not have complex multiplication.Modular form 216384.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.