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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 159120.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.p1 | 159120bk1 | \([0, 0, 0, -94672803, 354556914338]\) | \(31427652507069423952801/654426190080\) | \(1954106132759838720\) | \([2]\) | \(9338880\) | \(3.0391\) | \(\Gamma_0(N)\)-optimal |
159120.p2 | 159120bk2 | \([0, 0, 0, -94569123, 355372233122]\) | \(-31324512477868037557921/143427974919699600\) | \(-428273638262624290406400\) | \([2]\) | \(18677760\) | \(3.3857\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.p have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.p do not have complex multiplication.Modular form 159120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.