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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 150075g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150075.g2 | 150075g1 | \([1, -1, 1, -16880, -1316878]\) | \(-46694890801/39169575\) | \(-446165940234375\) | \([2]\) | \(565248\) | \(1.5087\) | \(\Gamma_0(N)\)-optimal |
150075.g1 | 150075g2 | \([1, -1, 1, -310505, -66501628]\) | \(290656902035521/86293125\) | \(982932626953125\) | \([2]\) | \(1130496\) | \(1.8553\) |
Rank
sage: E.rank()
The elliptic curves in class 150075g have rank \(0\).
Complex multiplication
The elliptic curves in class 150075g do not have complex multiplication.Modular form 150075.2.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 Cremona 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 Cremona labels.