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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 476850k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.k2 | 476850k1 | \([1, 1, 0, -3186375, -2185809375]\) | \(9486391169809/23842500\) | \(8992187326289062500\) | \([2]\) | \(17694720\) | \(2.5140\) | \(\Gamma_0(N)\)-optimal* |
476850.k1 | 476850k2 | \([1, 1, 0, -4414625, -347119125]\) | \(25228519578289/14463281250\) | \(5454819517785644531250\) | \([2]\) | \(35389440\) | \(2.8606\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850k have rank \(1\).
Complex multiplication
The elliptic curves in class 476850k do not have complex multiplication.Modular form 476850.2.a.k
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.