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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5700.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5700.r1 | 5700n2 | \([0, 1, 0, -86908, 8871188]\) | \(18148802937424/1947796875\) | \(7791187500000000\) | \([2]\) | \(27648\) | \(1.7835\) | |
5700.r2 | 5700n1 | \([0, 1, 0, -84533, 9431688]\) | \(267219216891904/3655125\) | \(913781250000\) | \([2]\) | \(13824\) | \(1.4369\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5700.r have rank \(0\).
Complex multiplication
The elliptic curves in class 5700.r do not have complex multiplication.Modular form 5700.2.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.