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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 253704y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253704.y1 | 253704y1 | \([0, -1, 0, -7703696, 8232508188]\) | \(55635379958596/24057\) | \(21863092279108608\) | \([2]\) | \(10321920\) | \(2.4777\) | \(\Gamma_0(N)\)-optimal |
253704.y2 | 253704y2 | \([0, -1, 0, -7665256, 8318690668]\) | \(-27403349188178/578739249\) | \(-1051920821917031565312\) | \([2]\) | \(20643840\) | \(2.8243\) |
Rank
sage: E.rank()
The elliptic curves in class 253704y have rank \(1\).
Complex multiplication
The elliptic curves in class 253704y do not have complex multiplication.Modular form 253704.2.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.