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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 364650fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.fl1 | 364650fl1 | \([1, 0, 0, -75513, -7270983]\) | \(3047678972871625/304559880768\) | \(4758748137000000\) | \([2]\) | \(3096576\) | \(1.7446\) | \(\Gamma_0(N)\)-optimal |
364650.fl2 | 364650fl2 | \([1, 0, 0, 93487, -35155983]\) | \(5783051584712375/37533175779528\) | \(-586455871555125000\) | \([2]\) | \(6193152\) | \(2.0912\) |
Rank
sage: E.rank()
The elliptic curves in class 364650fl have rank \(1\).
Complex multiplication
The elliptic curves in class 364650fl do not have complex multiplication.Modular form 364650.2.a.fl
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.