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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 28050.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.f1 | 28050s2 | \([1, 1, 0, -281325, 61912125]\) | \(-1260727040508389/121448888352\) | \(-237204860062500000\) | \([]\) | \(440000\) | \(2.0753\) | |
28050.f2 | 28050s1 | \([1, 1, 0, 550, -272250]\) | \(9393931/16427202\) | \(-32084378906250\) | \([]\) | \(88000\) | \(1.2706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28050.f have rank \(1\).
Complex multiplication
The elliptic curves in class 28050.f do not have complex multiplication.Modular form 28050.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.