Properties

Label 10830h
Number of curves $4$
Conductor $10830$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.h4 10830h1 \([1, 1, 0, -3617, -144411]\) \(-111284641/123120\) \(-5792288868720\) \([2]\) \(34560\) \(1.1436\) \(\Gamma_0(N)\)-optimal
10830.h3 10830h2 \([1, 1, 0, -68597, -6941319]\) \(758800078561/324900\) \(15285206736900\) \([2, 2]\) \(69120\) \(1.4902\)  
10830.h1 10830h3 \([1, 1, 0, -1097447, -442967949]\) \(3107086841064961/570\) \(26816152170\) \([2]\) \(138240\) \(1.8367\)  
10830.h2 10830h4 \([1, 1, 0, -79427, -4617201]\) \(1177918188481/488703750\) \(22991498466753750\) \([2]\) \(138240\) \(1.8367\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10830h have rank \(1\).

Complex multiplication

The elliptic curves in class 10830h do not have complex multiplication.

Modular form 10830.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + 2q^{13} - 4q^{14} - q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.