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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 97470.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97470.p1 | 97470ba2 | \([1, -1, 0, -517200, 143324000]\) | \(-16522921323/4000\) | \(-3704016302892000\) | \([]\) | \(1244160\) | \(1.9762\) | |
97470.p2 | 97470ba1 | \([1, -1, 0, 2640, 691456]\) | \(1601613/163840\) | \(-208115922862080\) | \([]\) | \(414720\) | \(1.4268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97470.p have rank \(1\).
Complex multiplication
The elliptic curves in class 97470.p do not have complex multiplication.Modular form 97470.2.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 LMFDB 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 LMFDB labels.