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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 59290.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.i1 | 59290cf2 | \([1, 0, 1, -7917033, -7553222932]\) | \(90315183328170247/11712800000000\) | \(7117229310514400000000\) | \([2]\) | \(5406720\) | \(2.9216\) | |
59290.i2 | 59290cf1 | \([1, 0, 1, 756247, -618068244]\) | \(78716413996793/317194240000\) | \(-192741628137963520000\) | \([2]\) | \(2703360\) | \(2.5750\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59290.i have rank \(0\).
Complex multiplication
The elliptic curves in class 59290.i do not have complex multiplication.Modular form 59290.2.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 LMFDB 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 LMFDB labels.