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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 182070.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.f1 | 182070df2 | \([1, -1, 0, -14165100, 2047381056]\) | \(3635924387633/2083248720\) | \(180098022559602240369360\) | \([2]\) | \(20054016\) | \(3.1520\) | |
182070.f2 | 182070df1 | \([1, -1, 0, 3521700, 253939536]\) | \(55874402767/32659200\) | \(-2823406193370209529600\) | \([2]\) | \(10027008\) | \(2.8054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182070.f have rank \(2\).
Complex multiplication
The elliptic curves in class 182070.f do not have complex multiplication.Modular form 182070.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.