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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 92400d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.s1 | 92400d1 | \([0, -1, 0, -157008, -23893488]\) | \(26752959989284/169785\) | \(2716560000000\) | \([2]\) | \(479232\) | \(1.5709\) | \(\Gamma_0(N)\)-optimal |
92400.s2 | 92400d2 | \([0, -1, 0, -154008, -24853488]\) | \(-12624273557282/1067664675\) | \(-34165269600000000\) | \([2]\) | \(958464\) | \(1.9175\) |
Rank
sage: E.rank()
The elliptic curves in class 92400d have rank \(1\).
Complex multiplication
The elliptic curves in class 92400d do not have complex multiplication.Modular form 92400.2.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 Cremona 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 Cremona labels.