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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 476850y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.y2 | 476850y1 | \([1, 1, 0, 5974925, -45266750375]\) | \(101847563/3881196\) | \(-898950765446582835937500\) | \([2]\) | \(81469440\) | \(3.2762\) | \(\Gamma_0(N)\)-optimal* |
476850.y1 | 476850y2 | \([1, 1, 0, -159838825, -744171706625]\) | \(1949845587157/95664294\) | \(22157471644618551011718750\) | \([2]\) | \(162938880\) | \(3.6227\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850y have rank \(1\).
Complex multiplication
The elliptic curves in class 476850y do not have complex multiplication.Modular form 476850.2.a.y
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.