Properties

Label 1248.a
Number of curves $2$
Conductor $1248$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1248.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.a1 1248a1 \([0, -1, 0, -14, -12]\) \(5088448/1053\) \(67392\) \([2]\) \(128\) \(-0.35830\) \(\Gamma_0(N)\)-optimal
1248.a2 1248a2 \([0, -1, 0, 31, -111]\) \(778688/1521\) \(-6230016\) \([2]\) \(256\) \(-0.011725\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1248.a have rank \(1\).

Complex multiplication

The elliptic curves in class 1248.a do not have complex multiplication.

Modular form 1248.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9} + 6 q^{11} - q^{13} + 2 q^{15} - 2 q^{17} + 6 q^{19} + O(q^{20})\)  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.