Properties

Label 18513.g
Number of curves $4$
Conductor $18513$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18513.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18513.g1 18513q3 \([1, -1, 1, -98759, -11920994]\) \(82483294977/17\) \(21954955473\) \([2]\) \(46080\) \(1.3716\)  
18513.g2 18513q2 \([1, -1, 1, -6194, -183752]\) \(20346417/289\) \(373234243041\) \([2, 2]\) \(23040\) \(1.0250\)  
18513.g3 18513q4 \([1, -1, 1, -749, -499562]\) \(-35937/83521\) \(-107864696238849\) \([2]\) \(46080\) \(1.3716\)  
18513.g4 18513q1 \([1, -1, 1, -749, 3556]\) \(35937/17\) \(21954955473\) \([2]\) \(11520\) \(0.67847\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18513.g have rank \(0\).

Complex multiplication

The elliptic curves in class 18513.g do not have complex multiplication.

Modular form 18513.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2 q^{5} - 4 q^{7} + 3 q^{8} - 2 q^{10} + 2 q^{13} + 4 q^{14} - q^{16} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.