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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 74025.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74025.r1 | 74025a2 | \([0, 0, 1, -7020, -226429]\) | \(-77750599680/16121\) | \(-7932741075\) | \([]\) | \(70848\) | \(0.89618\) | |
74025.r2 | 74025a1 | \([0, 0, 1, 30, -1064]\) | \(4423680/726761\) | \(-490563675\) | \([]\) | \(23616\) | \(0.34687\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74025.r have rank \(1\).
Complex multiplication
The elliptic curves in class 74025.r do not have complex multiplication.Modular form 74025.2.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.