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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 116032.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116032.g1 | 116032bu2 | \([0, 1, 0, -287009, -57950369]\) | \(169556172914/4353013\) | \(67125592252350464\) | \([2]\) | \(1327104\) | \(2.0110\) | |
116032.g2 | 116032bu1 | \([0, 1, 0, 3071, -2893185]\) | \(415292/469567\) | \(-3620476550053888\) | \([2]\) | \(663552\) | \(1.6644\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116032.g have rank \(0\).
Complex multiplication
The elliptic curves in class 116032.g do not have complex multiplication.Modular form 116032.2.a.g
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.