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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 38640.dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.dc1 | 38640db2 | \([0, 1, 0, -63680, -6202572]\) | \(6972359126281921/5071500000\) | \(20772864000000\) | \([2]\) | \(184320\) | \(1.4900\) | |
38640.dc2 | 38640db1 | \([0, 1, 0, -4800, -55500]\) | \(2986606123201/1421952000\) | \(5824315392000\) | \([2]\) | \(92160\) | \(1.1434\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.dc do not have complex multiplication.Modular form 38640.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.