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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 377520.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
377520.r1 | 377520r2 | \([0, -1, 0, -15762739736, -762131160959760]\) | \(-4076918475185827892929/2576893347639000\) | \(-273768353420103859679391744000\) | \([]\) | \(615859200\) | \(4.5899\) | |
377520.r2 | 377520r1 | \([0, -1, 0, 176038504, -4363390362384]\) | \(5678843727095231/80702844618240\) | \(-8573845288434969105703895040\) | \([]\) | \(205286400\) | \(4.0406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.r have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.r do not have complex multiplication.Modular form 377520.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.