Properties

Label 254100.b
Number of curves $2$
Conductor $254100$
CM no
Rank $0$
Graph

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

Elliptic curves in class 254100.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.b1 254100b2 \([0, -1, 0, -29246708, 60887901912]\) \(3123406998416/17787\) \(15755377753500000000\) \([2]\) \(21196800\) \(2.8749\)  
254100.b2 254100b1 \([0, -1, 0, -1794833, 987910662]\) \(-11550212096/922383\) \(-51064304683218750000\) \([2]\) \(10598400\) \(2.5283\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 254100.b have rank \(0\).

Complex multiplication

The elliptic curves in class 254100.b do not have complex multiplication.

Modular form 254100.2.a.b

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