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Properties

Label 380926bb
Number of curves $2$
Conductor $380926$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 380926bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380926.bb2 380926bb1 \([1, 1, 0, -9341140, 4109097504]\) \(391197625/194672\) \(44857050027389475909488\) \([]\) \(31135104\) \(3.0394\) \(\Gamma_0(N)\)-optimal
380926.bb1 380926bb2 \([1, 1, 0, -615965795, 5883879228557]\) \(112167304419625/94208\) \(21707759559568442028032\) \([]\) \(93405312\) \(3.5887\)  

Rank

sage: E.rank()
 

The elliptic curves in class 380926bb have rank \(1\).

Complex multiplication

The elliptic curves in class 380926bb do not have complex multiplication.

Modular form 380926.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.