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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 65088dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65088.bo2 | 65088dg1 | \([0, 0, 0, -956748, 362678416]\) | \(-506814405937489/4048994304\) | \(-773774861301448704\) | \([]\) | \(774144\) | \(2.2605\) | \(\Gamma_0(N)\)-optimal |
65088.bo1 | 65088dg2 | \([0, 0, 0, -4101708, -35483575664]\) | \(-39934705050538129/2823126576537804\) | \(-539507890401066120904704\) | \([]\) | \(5419008\) | \(3.2335\) |
Rank
sage: E.rank()
The elliptic curves in class 65088dg have rank \(1\).
Complex multiplication
The elliptic curves in class 65088dg do not have complex multiplication.Modular form 65088.2.a.dg
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.