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Properties

Label 281775cb
Number of curves $2$
Conductor $281775$
CM no
Rank $1$
Graph

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

Elliptic curves in class 281775cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.cb1 281775cb1 \([1, 0, 1, -1352960876, -19153140431227]\) \(147815204204011553/15178486401\) \(28124757355205969020265625\) \([2]\) \(108625920\) \(3.9161\) \(\Gamma_0(N)\)-optimal
281775.cb2 281775cb2 \([1, 0, 1, -1249173751, -22215068192977]\) \(-116340772335201233/47730591665289\) \(-88441711086437960840822390625\) \([2]\) \(217251840\) \(4.2627\)  

Rank

sage: E.rank()
 

The elliptic curves in class 281775cb have rank \(1\).

Complex multiplication

The elliptic curves in class 281775cb do not have complex multiplication.

Modular form 281775.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} - 3 q^{8} + q^{9} - q^{12} + q^{13} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.