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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 114240.fp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
114240.fp1 | 114240iu2 | \([0, 1, 0, -3459041, -2362118241]\) | \(17460273607244690041/918397653311250\) | \(240752434429624320000\) | \([2]\) | \(5898240\) | \(2.6679\) | |
114240.fp2 | 114240iu1 | \([0, 1, 0, 140959, -146678241]\) | \(1181569139409959/36161310937500\) | \(-9479470694400000000\) | \([2]\) | \(2949120\) | \(2.3213\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 114240.fp have rank \(0\).
Complex multiplication
The elliptic curves in class 114240.fp do not have complex multiplication.Modular form 114240.2.a.fp
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.