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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 406800.dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
406800.dc1 | 406800dc2 | \([0, 0, 0, -25635675, -554430869750]\) | \(-39934705050538129/2823126576537804\) | \(-131715793554947783424000000\) | \([]\) | \(94832640\) | \(3.6916\) | |
406800.dc2 | 406800dc1 | \([0, 0, 0, -5979675, 5666850250]\) | \(-506814405937489/4048994304\) | \(-188909878247424000000\) | \([]\) | \(13547520\) | \(2.7187\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 406800.dc have rank \(2\).
Complex multiplication
The elliptic curves in class 406800.dc do not have complex multiplication.Modular form 406800.2.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 LMFDB 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 LMFDB labels.