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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 66240.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.r1 | 66240d2 | \([0, 0, 0, -604908, -181050768]\) | \(37953380909016/8265625\) | \(5331101184000000\) | \([2]\) | \(663552\) | \(2.0118\) | |
66240.r2 | 66240d1 | \([0, 0, 0, -33588, -3484512]\) | \(-51978639168/34980125\) | \(-2820152526336000\) | \([2]\) | \(331776\) | \(1.6653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.r have rank \(1\).
Complex multiplication
The elliptic curves in class 66240.r do not have complex multiplication.Modular form 66240.2.a.r
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.