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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 227430.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227430.g1 | 227430ge2 | \([1, -1, 0, -213960, 38058566]\) | \(852780481587/2280950\) | \(2897351161207650\) | \([2]\) | \(1658880\) | \(1.8412\) | |
227430.g2 | 227430ge1 | \([1, -1, 0, -8190, 1061120]\) | \(-47832147/353780\) | \(-449385078064860\) | \([2]\) | \(829440\) | \(1.4946\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227430.g have rank \(2\).
Complex multiplication
The elliptic curves in class 227430.g do not have complex multiplication.Modular form 227430.2.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.