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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 169756.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169756.d1 | 169756d1 | \([0, 1, 0, -3194, 87109]\) | \(-87808/31\) | \(-1272600298864\) | \([]\) | \(290304\) | \(1.0337\) | \(\Gamma_0(N)\)-optimal |
169756.d2 | 169756d2 | \([0, 1, 0, 24186, -849287]\) | \(38112512/29791\) | \(-1222968887208304\) | \([]\) | \(870912\) | \(1.5830\) |
Rank
sage: E.rank()
The elliptic curves in class 169756.d have rank \(2\).
Complex multiplication
The elliptic curves in class 169756.d do not have complex multiplication.Modular form 169756.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.