Properties

Label 58800gb
Number of curves $6$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800gb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.m6 58800gb1 \([0, -1, 0, 19192, -231888]\) \(103823/63\) \(-474360768000000\) \([2]\) \(196608\) \(1.5053\) \(\Gamma_0(N)\)-optimal
58800.m5 58800gb2 \([0, -1, 0, -78808, -1799888]\) \(7189057/3969\) \(29884728384000000\) \([2, 2]\) \(393216\) \(1.8519\)  
58800.m3 58800gb3 \([0, -1, 0, -764808, 256136112]\) \(6570725617/45927\) \(345808999872000000\) \([2]\) \(786432\) \(2.1985\)  
58800.m2 58800gb4 \([0, -1, 0, -960808, -361655888]\) \(13027640977/21609\) \(162705743424000000\) \([2, 2]\) \(786432\) \(2.1985\)  
58800.m4 58800gb5 \([0, -1, 0, -666808, -587447888]\) \(-4354703137/17294403\) \(-130218829987008000000\) \([2]\) \(1572864\) \(2.5450\)  
58800.m1 58800gb6 \([0, -1, 0, -15366808, -23180759888]\) \(53297461115137/147\) \(1106841792000000\) \([2]\) \(1572864\) \(2.5450\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800gb have rank \(1\).

Complex multiplication

The elliptic curves in class 58800gb do not have complex multiplication.

Modular form 58800.2.a.gb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.