Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.g4 10830g1 \([1, 1, 0, 3369928, 5064449856]\) \(89962967236397039/287450726400000\) \(-13523372667577958400000\) \([2]\) \(864000\) \(2.9298\) \(\Gamma_0(N)\)-optimal
10830.g3 10830g2 \([1, 1, 0, -31748152, 59307836224]\) \(75224183150104868881/11219310000000000\) \(527822323162110000000000\) \([2]\) \(1728000\) \(3.2763\)  
10830.g2 10830g3 \([1, 1, 0, -1191828872, 15836364428016]\) \(-3979640234041473454886161/1471455901872240\) \(-69225939256229080243440\) \([2]\) \(4320000\) \(3.7345\)  
10830.g1 10830g4 \([1, 1, 0, -19069263652, 1013550971091124]\) \(16300610738133468173382620881/2228489100\) \(104841233008397100\) \([2]\) \(8640000\) \(4.0810\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10830.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.