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SageMath
E = EllipticCurve("iy1")
E.isogeny_class()
Elliptic curves in class 78400iy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.kv1 | 78400iy1 | \([0, 0, 0, -210700, 37226000]\) | \(-5154200289/20\) | \(-4014080000000\) | \([]\) | \(552960\) | \(1.6316\) | \(\Gamma_0(N)\)-optimal |
78400.kv2 | 78400iy2 | \([0, 0, 0, 1469300, -353206000]\) | \(1747829720511/1280000000\) | \(-256901120000000000000\) | \([]\) | \(3870720\) | \(2.6046\) |
Rank
sage: E.rank()
The elliptic curves in class 78400iy have rank \(1\).
Complex multiplication
The elliptic curves in class 78400iy do not have complex multiplication.Modular form 78400.2.a.iy
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.