Properties

Label 38808.b
Number of curves $2$
Conductor $38808$
CM no
Rank $1$
Graph

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

Elliptic curves in class 38808.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38808.b1 38808cq2 \([0, 0, 0, -24960747, -47997440890]\) \(9791533777258802/427901859\) \(75160540395763587072\) \([2]\) \(2949120\) \(2.8921\)  
38808.b2 38808cq1 \([0, 0, 0, -1481907, -828451330]\) \(-4097989445764/1004475087\) \(-88217530217602587648\) \([2]\) \(1474560\) \(2.5455\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38808.b have rank \(1\).

Complex multiplication

The elliptic curves in class 38808.b do not have complex multiplication.

Modular form 38808.2.a.b

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + q^{11} + 2 q^{13} - 2 q^{19} + O(q^{20})\) 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.