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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 34496.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34496.dg1 | 34496bq2 | \([0, -1, 0, -4467297, -2547529375]\) | \(1278763167594532/375974556419\) | \(2898855892624272982016\) | \([2]\) | \(1474560\) | \(2.8241\) | |
34496.dg2 | 34496bq1 | \([0, -1, 0, 750223, -265386127]\) | \(24226243449392/29774625727\) | \(-57392413772281004032\) | \([2]\) | \(737280\) | \(2.4775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34496.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 34496.dg do not have complex multiplication.Modular form 34496.2.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.