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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 378560dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
378560.dq1 | 378560dq1 | \([0, 0, 0, -9141548, -10638366128]\) | \(267080942160036/1990625\) | \(629693917798400000\) | \([2]\) | \(12042240\) | \(2.5913\) | \(\Gamma_0(N)\)-optimal |
378560.dq2 | 378560dq2 | \([0, 0, 0, -8952268, -11099982192]\) | \(-125415986034978/11552734375\) | \(-7308947260160000000000\) | \([2]\) | \(24084480\) | \(2.9379\) |
Rank
sage: E.rank()
The elliptic curves in class 378560dq have rank \(0\).
Complex multiplication
The elliptic curves in class 378560dq do not have complex multiplication.Modular form 378560.2.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 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.