Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1248.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.h1 1248d2 \([0, 1, 0, -1313, 17871]\) \(61162984000/41067\) \(168210432\) \([2]\) \(640\) \(0.51681\)  
1248.h2 1248d1 \([0, 1, 0, -98, 132]\) \(1643032000/767637\) \(49128768\) \([2]\) \(320\) \(0.17024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1248.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{7} + q^{9} - 4q^{11} + q^{13} - 6q^{17} - 6q^{19} + O(q^{20})\)  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.