Properties

Label 10920.g
Number of curves $4$
Conductor $10920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 10920.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10920.g1 10920c4 \([0, -1, 0, -861336, 307935036]\) \(69014771940559650916/9797607421875\) \(10032750000000000\) \([2]\) \(184320\) \(2.0864\)  
10920.g2 10920c3 \([0, -1, 0, -351216, -76944420]\) \(4678944235881273796/202428825314625\) \(207287117122176000\) \([2]\) \(184320\) \(2.0864\)  
10920.g3 10920c2 \([0, -1, 0, -58716, 3902580]\) \(87450143958975184/25164018140625\) \(6441988644000000\) \([2, 2]\) \(92160\) \(1.7399\)  
10920.g4 10920c1 \([0, -1, 0, 9729, 398196]\) \(6364491337435136/8034291412875\) \(-128548662606000\) \([2]\) \(46080\) \(1.3933\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10920.g have rank \(0\).

Complex multiplication

The elliptic curves in class 10920.g do not have complex multiplication.

Modular form 10920.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 4 q^{11} - q^{13} + q^{15} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.