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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 389376.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389376.g1 | 389376g1 | \([0, 0, 0, -11154, -509704]\) | \(-85184/13\) | \(-23420758473216\) | \([]\) | \(967680\) | \(1.2946\) | \(\Gamma_0(N)\)-optimal |
389376.g2 | 389376g2 | \([0, 0, 0, -11154, 39352664]\) | \(-85184/371293\) | \(-668920282753522176\) | \([]\) | \(4838400\) | \(2.0993\) |
Rank
sage: E.rank()
The elliptic curves in class 389376.g have rank \(0\).
Complex multiplication
The elliptic curves in class 389376.g do not have complex multiplication.Modular form 389376.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.