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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 76230.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.dg1 | 76230cv1 | \([1, -1, 1, -22789163, 41874012667]\) | \(37537160298467283/5519360000\) | \(192458069533255680000\) | \([2]\) | \(5160960\) | \(2.9064\) | \(\Gamma_0(N)\)-optimal |
76230.dg2 | 76230cv2 | \([1, -1, 1, -20698283, 49867028731]\) | \(-28124139978713043/14526050000000\) | \(-506518063859496150000000\) | \([2]\) | \(10321920\) | \(3.2530\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.dg do not have complex multiplication.Modular form 76230.2.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.