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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 14400.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.f1 | 14400bt3 | \([0, 0, 0, -29100, 1910000]\) | \(7301384/3\) | \(1119744000000\) | \([2]\) | \(32768\) | \(1.2744\) | |
14400.f2 | 14400bt2 | \([0, 0, 0, -2100, 20000]\) | \(21952/9\) | \(419904000000\) | \([2, 2]\) | \(16384\) | \(0.92780\) | |
14400.f3 | 14400bt1 | \([0, 0, 0, -975, -11500]\) | \(140608/3\) | \(2187000000\) | \([2]\) | \(8192\) | \(0.58123\) | \(\Gamma_0(N)\)-optimal |
14400.f4 | 14400bt4 | \([0, 0, 0, 6900, 146000]\) | \(97336/81\) | \(-30233088000000\) | \([2]\) | \(32768\) | \(1.2744\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.f have rank \(2\).
Complex multiplication
The elliptic curves in class 14400.f do not have complex multiplication.Modular form 14400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.