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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 76050fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.eo2 | 76050fr1 | \([1, -1, 1, -590180, 151834947]\) | \(3307949/468\) | \(3216351719039062500\) | \([2]\) | \(1720320\) | \(2.2772\) | \(\Gamma_0(N)\)-optimal |
76050.eo1 | 76050fr2 | \([1, -1, 1, -2491430, -1361560053]\) | \(248858189/27378\) | \(188156575563785156250\) | \([2]\) | \(3440640\) | \(2.6237\) |
Rank
sage: E.rank()
The elliptic curves in class 76050fr have rank \(0\).
Complex multiplication
The elliptic curves in class 76050fr do not have complex multiplication.Modular form 76050.2.a.fr
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.