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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 44100.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.dg1 | 44100dn2 | \([0, 0, 0, -25467015, -49450430050]\) | \(665567485783184/257298363\) | \(706159441093117536000\) | \([2]\) | \(3096576\) | \(2.9659\) | |
44100.dg2 | 44100dn1 | \([0, 0, 0, -1355340, -1010074975]\) | \(-1605176213504/1640558367\) | \(-281408654823368814000\) | \([2]\) | \(1548288\) | \(2.6193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44100.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 44100.dg do not have complex multiplication.Modular form 44100.2.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 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.