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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 51600.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.dq1 | 51600di4 | \([0, 1, 0, -2073008, 990587988]\) | \(15393836938735081/2275690697640\) | \(145644204648960000000\) | \([2]\) | \(1658880\) | \(2.5936\) | |
51600.dq2 | 51600di3 | \([0, 1, 0, -1993008, 1082267988]\) | \(13679527032530281/381633600\) | \(24424550400000000\) | \([2]\) | \(829440\) | \(2.2471\) | |
51600.dq3 | 51600di2 | \([0, 1, 0, -543008, -154032012]\) | \(276670733768281/336980250\) | \(21566736000000000\) | \([2]\) | \(552960\) | \(2.0443\) | |
51600.dq4 | 51600di1 | \([0, 1, 0, -43008, -1032012]\) | \(137467988281/72562500\) | \(4644000000000000\) | \([2]\) | \(276480\) | \(1.6978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.dq have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.dq do not have complex multiplication.Modular form 51600.2.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.