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Properties

Label 367770.bl
Number of curves $2$
Conductor $367770$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 367770.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
367770.bl1 367770bl2 \([1, 0, 0, -46440338855, -3852047375777835]\) \(11076686187617538707593043636859463921/16864347774313526578260\) \(16864347774313526578260\) \([]\) \(613119360\) \(4.4243\)  
367770.bl2 367770bl1 \([1, 0, 0, -57317555, 127028237025]\) \(20825080158898735138027980721/5080200043046319360000000\) \(5080200043046319360000000\) \([7]\) \(87588480\) \(3.4513\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 367770.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 367770.bl do not have complex multiplication.

Modular form 367770.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} + q^{12} - q^{13} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.