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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5850.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.q1 | 5850h1 | \([1, -1, 0, -5742, -168584]\) | \(-2941225/52\) | \(-370195312500\) | \([]\) | \(8640\) | \(1.0169\) | \(\Gamma_0(N)\)-optimal |
5850.q2 | 5850h2 | \([1, -1, 0, 22383, -815459]\) | \(174196775/140608\) | \(-1001008125000000\) | \([]\) | \(25920\) | \(1.5662\) |
Rank
sage: E.rank()
The elliptic curves in class 5850.q have rank \(0\).
Complex multiplication
The elliptic curves in class 5850.q do not have complex multiplication.Modular form 5850.2.a.q
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.