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Properties

Label 74382.bc
Number of curves $2$
Conductor $74382$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 74382.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74382.bc1 74382u2 \([1, 1, 1, -1493800617758, 702727065966594395]\) \(-3133382230165522315000208250857964625/153574604080128\) \(-18067898595422979072\) \([]\) \(431101440\) \(5.0874\)  
74382.bc2 74382u1 \([1, 1, 1, -18441820958, 963971259390299]\) \(-5895856113332931416918127084625/215771481613620039647232\) \(-25385299040360784044457197568\) \([]\) \(143700480\) \(4.5381\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 74382.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 74382.bc do not have complex multiplication.

Modular form 74382.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{11} - q^{12} + q^{13} + q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.