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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 33930y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33930.t1 | 33930y1 | \([1, -1, 1, -7493, -210499]\) | \(63812982460681/10201800960\) | \(7437112899840\) | \([2]\) | \(61440\) | \(1.1922\) | \(\Gamma_0(N)\)-optimal |
33930.t2 | 33930y2 | \([1, -1, 1, 13387, -1187683]\) | \(363979050334199/1041836936400\) | \(-759499126635600\) | \([2]\) | \(122880\) | \(1.5388\) |
Rank
sage: E.rank()
The elliptic curves in class 33930y have rank \(0\).
Complex multiplication
The elliptic curves in class 33930y do not have complex multiplication.Modular form 33930.2.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.