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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3042.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3042.g1 | 3042h2 | \([1, -1, 0, -2898, -60332]\) | \(-1680914269/32768\) | \(-52481654784\) | \([]\) | \(3600\) | \(0.85045\) | |
3042.g2 | 3042h1 | \([1, -1, 0, 27, 157]\) | \(1331/8\) | \(-12812904\) | \([]\) | \(720\) | \(0.045728\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3042.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3042.g do not have complex multiplication.Modular form 3042.2.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.