Properties

Label 7744.n
Number of curves $2$
Conductor $7744$
CM \(\Q(\sqrt{-11}) \)
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 7744.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
7744.n1 7744s2 \([0, -1, 0, -3549, 84691]\) \(-32768\) \(-150908652224\) \([]\) \(6336\) \(0.92245\)   \(-11\)
7744.n2 7744s1 \([0, -1, 0, -29, -53]\) \(-32768\) \(-85184\) \([]\) \(576\) \(-0.27650\) \(\Gamma_0(N)\)-optimal \(-11\)

Rank

sage: E.rank()
 

The elliptic curves in class 7744.n have rank \(0\).

Complex multiplication

Each elliptic curve in class 7744.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 7744.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} - 2 q^{9} - 3 q^{15} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.