Properties

Label 18810.c
Number of curves $4$
Conductor $18810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 18810.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18810.c1 18810d4 \([1, -1, 0, -44061345, 111468497571]\) \(12976854634417729473922321/148112152782766327650\) \(107973759378636652856850\) \([2]\) \(2560000\) \(3.2329\)  
18810.c2 18810d2 \([1, -1, 0, -4094595, -3187970379]\) \(10414276373665867414321/301547812500000\) \(219828355312500000\) \([2]\) \(512000\) \(2.4281\)  
18810.c3 18810d3 \([1, -1, 0, -577575, 4420152585]\) \(-29229525625065721201/11560253601080069820\) \(-8427424875187370898780\) \([2]\) \(1280000\) \(2.8863\)  
18810.c4 18810d1 \([1, -1, 0, -245475, -54016875]\) \(-2243980016705847601/434411683200000\) \(-316686117052800000\) \([2]\) \(256000\) \(2.0816\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18810.c have rank \(0\).

Complex multiplication

The elliptic curves in class 18810.c do not have complex multiplication.

Modular form 18810.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 2 q^{7} - q^{8} + q^{10} - q^{11} - 6 q^{13} + 2 q^{14} + q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.