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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 284592g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.g2 | 284592g1 | \([0, -1, 0, -32160, -2002944]\) | \(5735339/588\) | \(377140844838912\) | \([2]\) | \(1769472\) | \(1.5326\) | \(\Gamma_0(N)\)-optimal |
284592.g1 | 284592g2 | \([0, -1, 0, -118400, 13520256]\) | \(286191179/43218\) | \(27719852095660032\) | \([2]\) | \(3538944\) | \(1.8791\) |
Rank
sage: E.rank()
The elliptic curves in class 284592g have rank \(1\).
Complex multiplication
The elliptic curves in class 284592g do not have complex multiplication.Modular form 284592.2.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.