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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 14490k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.h4 | 14490k1 | \([1, -1, 0, -330, 1700]\) | \(5461074081/1610000\) | \(1173690000\) | \([2]\) | \(8192\) | \(0.44605\) | \(\Gamma_0(N)\)-optimal |
14490.h2 | 14490k2 | \([1, -1, 0, -4830, 130400]\) | \(17095749786081/2592100\) | \(1889640900\) | \([2, 2]\) | \(16384\) | \(0.79263\) | |
14490.h1 | 14490k3 | \([1, -1, 0, -77280, 8288270]\) | \(70016546394529281/1610\) | \(1173690\) | \([2]\) | \(32768\) | \(1.1392\) | |
14490.h3 | 14490k4 | \([1, -1, 0, -4380, 155330]\) | \(-12748946194881/6718982410\) | \(-4898138176890\) | \([2]\) | \(32768\) | \(1.1392\) |
Rank
sage: E.rank()
The elliptic curves in class 14490k have rank \(1\).
Complex multiplication
The elliptic curves in class 14490k do not have complex multiplication.Modular form 14490.2.a.k
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 Cremona 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 Cremona labels.