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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 248430.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.f1 | 248430f2 | \([1, 1, 0, -7295733, 16067300397]\) | \(-447502578601/903544320\) | \(-86713061284145678753280\) | \([]\) | \(29113344\) | \(3.0907\) | |
248430.f2 | 248430f1 | \([1, 1, 0, 778242, -473044788]\) | \(543164999/1323000\) | \(-126968182456091067000\) | \([]\) | \(9704448\) | \(2.5414\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248430.f have rank \(0\).
Complex multiplication
The elliptic curves in class 248430.f do not have complex multiplication.Modular form 248430.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.