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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3900.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3900.d1 | 3900a2 | \([0, -1, 0, -5533, -179063]\) | \(-4684079104/823875\) | \(-3295500000000\) | \([]\) | \(5184\) | \(1.1277\) | |
3900.d2 | 3900a1 | \([0, -1, 0, 467, 937]\) | \(2809856/1755\) | \(-7020000000\) | \([]\) | \(1728\) | \(0.57841\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3900.d have rank \(0\).
Complex multiplication
The elliptic curves in class 3900.d do not have complex multiplication.Modular form 3900.2.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.