Properties

Label 18480a
Number of curves $4$
Conductor $18480$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 18480a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.c3 18480a1 \([0, -1, 0, -511, 4606]\) \(924093773824/3565485\) \(57047760\) \([2]\) \(6144\) \(0.34653\) \(\Gamma_0(N)\)-optimal
18480.c2 18480a2 \([0, -1, 0, -756, 0]\) \(186906097744/108056025\) \(27662342400\) \([2, 2]\) \(12288\) \(0.69310\)  
18480.c1 18480a3 \([0, -1, 0, -8456, -295680]\) \(65308549273636/204604785\) \(209515299840\) \([2]\) \(24576\) \(1.0397\)  
18480.c4 18480a4 \([0, -1, 0, 3024, -3024]\) \(2985557859644/1729468125\) \(-1770975360000\) \([2]\) \(24576\) \(1.0397\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18480a have rank \(1\).

Complex multiplication

The elliptic curves in class 18480a do not have complex multiplication.

Modular form 18480.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - q^{11} - 2 q^{13} + q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.