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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 16660.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16660.g1 | 16660h1 | \([0, 0, 0, -1372, -19551]\) | \(151732224/85\) | \(160002640\) | \([2]\) | \(6912\) | \(0.52141\) | \(\Gamma_0(N)\)-optimal |
16660.g2 | 16660h2 | \([0, 0, 0, -1127, -26754]\) | \(-5256144/7225\) | \(-217603590400\) | \([2]\) | \(13824\) | \(0.86798\) |
Rank
sage: E.rank()
The elliptic curves in class 16660.g have rank \(0\).
Complex multiplication
The elliptic curves in class 16660.g do not have complex multiplication.Modular form 16660.2.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.