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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5070i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.j1 | 5070i1 | \([1, 0, 1, -849, 9466]\) | \(-2365581049/6750\) | \(-192786750\) | \([3]\) | \(3024\) | \(0.46139\) | \(\Gamma_0(N)\)-optimal |
5070.j2 | 5070i2 | \([1, 0, 1, 1686, 49012]\) | \(18573478391/46875000\) | \(-1338796875000\) | \([]\) | \(9072\) | \(1.0107\) |
Rank
sage: E.rank()
The elliptic curves in class 5070i have rank \(0\).
Complex multiplication
The elliptic curves in class 5070i do not have complex multiplication.Modular form 5070.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.