Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 18480.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.m1 18480bu3 \([0, -1, 0, -416696, -103386000]\) \(1953542217204454969/170843779260\) \(699776119848960\) \([2]\) \(122880\) \(1.8898\)  
18480.m2 18480bu4 \([0, -1, 0, -151096, 21501040]\) \(93137706732176569/5369647977540\) \(21994078116003840\) \([2]\) \(122880\) \(1.8898\)  
18480.m3 18480bu2 \([0, -1, 0, -27896, -1364880]\) \(586145095611769/140040608400\) \(573606332006400\) \([2, 2]\) \(61440\) \(1.5432\)  
18480.m4 18480bu1 \([0, -1, 0, 4104, -136080]\) \(1865864036231/2993760000\) \(-12262440960000\) \([2]\) \(30720\) \(1.1966\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 18480.2.a.m

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 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.