Properties

Label 17424.cb
Number of curves $2$
Conductor $17424$
CM \(\Q(\sqrt{-11}) \)
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 17424.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
17424.cb1 17424bl2 \([0, 0, 0, -127776, -18037712]\) \(-32768\) \(-7040794078162944\) \([]\) \(95040\) \(1.8183\)   \(-11\)
17424.cb2 17424bl1 \([0, 0, 0, -1056, 13552]\) \(-32768\) \(-3974344704\) \([]\) \(8640\) \(0.61938\) \(\Gamma_0(N)\)-optimal \(-11\)

Rank

sage: E.rank()
 

The elliptic curves in class 17424.cb have rank \(1\).

Complex multiplication

Each elliptic curve in class 17424.cb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 17424.2.a.cb

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