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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 77616.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.dq1 | 77616ex3 | \([0, 0, 0, -568155, 164203018]\) | \(57736239625/255552\) | \(89774914575532032\) | \([2]\) | \(829440\) | \(2.1053\) | |
77616.dq2 | 77616ex4 | \([0, 0, 0, -285915, 327394186]\) | \(-7357983625/127552392\) | \(-44808904237512425472\) | \([2]\) | \(1658880\) | \(2.4519\) | |
77616.dq3 | 77616ex1 | \([0, 0, 0, -38955, -2791334]\) | \(18609625/1188\) | \(417342061559808\) | \([2]\) | \(276480\) | \(1.5560\) | \(\Gamma_0(N)\)-optimal |
77616.dq4 | 77616ex2 | \([0, 0, 0, 31605, -11780678]\) | \(9938375/176418\) | \(-61975296141631488\) | \([2]\) | \(552960\) | \(1.9026\) |
Rank
sage: E.rank()
The elliptic curves in class 77616.dq have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.dq do not have complex multiplication.Modular form 77616.2.a.dq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.