Properties

Label 1440.g
Number of curves $4$
Conductor $1440$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1440.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.g1 1440g2 \([0, 0, 0, -32412, -2245984]\) \(1261112198464/675\) \(2015539200\) \([2]\) \(3072\) \(1.1149\)  
1440.g2 1440g3 \([0, 0, 0, -4467, 63974]\) \(26410345352/10546875\) \(3936600000000\) \([4]\) \(3072\) \(1.1149\)  
1440.g3 1440g1 \([0, 0, 0, -2037, -34684]\) \(20034997696/455625\) \(21257640000\) \([2, 2]\) \(1536\) \(0.76837\) \(\Gamma_0(N)\)-optimal
1440.g4 1440g4 \([0, 0, 0, 213, -107134]\) \(2863288/13286025\) \(-4958982259200\) \([2]\) \(3072\) \(1.1149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1440.g have rank \(1\).

Complex multiplication

The elliptic curves in class 1440.g do not have complex multiplication.

Modular form 1440.2.a.g

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