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Properties

Label 259350.gz
Number of curves $2$
Conductor $259350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gz1")
 
E.isogeny_class()
 

Elliptic curves in class 259350.gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259350.gz1 259350gz1 \([1, 0, 0, -1204188, 508510992]\) \(12359092816971484921/116188800000\) \(1815450000000000\) \([2]\) \(6144000\) \(2.0908\) \(\Gamma_0(N)\)-optimal
259350.gz2 259350gz2 \([1, 0, 0, -1176188, 533290992]\) \(-11516856136356002041/1201114687500000\) \(-18767416992187500000\) \([2]\) \(12288000\) \(2.4374\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259350.gz have rank \(0\).

Complex multiplication

The elliptic curves in class 259350.gz do not have complex multiplication.

Modular form 259350.2.a.gz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + 4 q^{11} + q^{12} + q^{13} + q^{14} + q^{16} + 6 q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

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.