Properties

Label 1440.b
Number of curves $2$
Conductor $1440$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1440.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.b1 1440a2 \([0, 0, 0, -243, -1242]\) \(157464/25\) \(251942400\) \([2]\) \(384\) \(0.33467\)  
1440.b2 1440a1 \([0, 0, 0, 27, -108]\) \(1728/5\) \(-6298560\) \([2]\) \(192\) \(-0.011906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1440.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.