Properties

Label 1296.a
Number of curves $2$
Conductor $1296$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1296.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1296.a1 1296i1 \([0, 0, 0, -39, -94]\) \(-316368\) \(-20736\) \([]\) \(144\) \(-0.30456\) \(\Gamma_0(N)\)-optimal
1296.a2 1296i2 \([0, 0, 0, 81, -486]\) \(432\) \(-136048896\) \([]\) \(432\) \(0.24475\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1296.a have rank \(0\).

Complex multiplication

The elliptic curves in class 1296.a do not have complex multiplication.

Modular form 1296.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} - 2 q^{7} - 6 q^{11} + 5 q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.