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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4026.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4026.d1 | 4026e2 | \([1, 0, 1, -114, 454]\) | \(161789533849/736758\) | \(736758\) | \([2]\) | \(1184\) | \(-0.023059\) | |
4026.d2 | 4026e1 | \([1, 0, 1, -4, 14]\) | \(-4826809/88572\) | \(-88572\) | \([2]\) | \(592\) | \(-0.36963\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4026.d have rank \(0\).
Complex multiplication
The elliptic curves in class 4026.d do not have complex multiplication.Modular form 4026.2.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.