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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 84700p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84700.j2 | 84700p1 | \([0, -1, 0, -16133, 3875137]\) | \(-65536/875\) | \(-6200463500000000\) | \([]\) | \(388800\) | \(1.7119\) | \(\Gamma_0(N)\)-optimal |
84700.j1 | 84700p2 | \([0, -1, 0, -2436133, 1464345137]\) | \(-225637236736/1715\) | \(-12152908460000000\) | \([]\) | \(1166400\) | \(2.2612\) |
Rank
sage: E.rank()
The elliptic curves in class 84700p have rank \(0\).
Complex multiplication
The elliptic curves in class 84700p do not have complex multiplication.Modular form 84700.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.