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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 91035.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.m1 | 91035y2 | \([1, -1, 1, -1556753, 610277186]\) | \(23711636464489/4590075735\) | \(80768293661446608735\) | \([2]\) | \(2654208\) | \(2.5369\) | |
91035.m2 | 91035y1 | \([1, -1, 1, 198922, 56186156]\) | \(49471280711/106269975\) | \(-1869957064705074975\) | \([2]\) | \(1327104\) | \(2.1903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.m have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.m do not have complex multiplication.Modular form 91035.2.a.m
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.