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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7406.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7406.d1 | 7406b2 | \([1, -1, 0, -126001, -17129673]\) | \(1494447319737/5411854\) | \(801148618028206\) | \([2]\) | \(50688\) | \(1.7208\) | |
7406.d2 | 7406b1 | \([1, -1, 0, -4331, -509551]\) | \(-60698457/725788\) | \(-107442671805532\) | \([2]\) | \(25344\) | \(1.3742\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7406.d have rank \(0\).
Complex multiplication
The elliptic curves in class 7406.d do not have complex multiplication.Modular form 7406.2.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.