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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 47025.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47025.r1 | 47025bc2 | \([1, -1, 1, -6980, -209478]\) | \(3301293169/218405\) | \(2487769453125\) | \([2]\) | \(73728\) | \(1.1280\) | |
47025.r2 | 47025bc1 | \([1, -1, 1, -1355, 15522]\) | \(24137569/5225\) | \(59516015625\) | \([2]\) | \(36864\) | \(0.78141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47025.r have rank \(1\).
Complex multiplication
The elliptic curves in class 47025.r do not have complex multiplication.Modular form 47025.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.