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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 70560dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.p1 | 70560dc1 | \([0, 0, 0, -273, 1568]\) | \(140608/15\) | \(240045120\) | \([2]\) | \(20480\) | \(0.34240\) | \(\Gamma_0(N)\)-optimal |
70560.p2 | 70560dc2 | \([0, 0, 0, 357, 7742]\) | \(39304/225\) | \(-28805414400\) | \([2]\) | \(40960\) | \(0.68897\) |
Rank
sage: E.rank()
The elliptic curves in class 70560dc have rank \(2\).
Complex multiplication
The elliptic curves in class 70560dc do not have complex multiplication.Modular form 70560.2.a.dc
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.