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Properties

Label 775.b
Number of curves $2$
Conductor $775$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 775.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
775.b1 775b2 \([1, 0, 1, -651, -6427]\) \(1948441249/4805\) \(75078125\) \([2]\) \(384\) \(0.38912\)  
775.b2 775b1 \([1, 0, 1, -26, -177]\) \(-117649/775\) \(-12109375\) \([2]\) \(192\) \(0.042542\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 775.b have rank \(0\).

Complex multiplication

The elliptic curves in class 775.b do not have complex multiplication.

Modular form 775.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - 4 q^{7} - 3 q^{8} + q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{14} - q^{16} + 8 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.