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Properties

Label 407330.f
Number of curves $2$
Conductor $407330$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 407330.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
407330.f1 407330f1 \([1, -1, 0, -174140, -20673444]\) \(324242703/84700\) \(152557630425916100\) \([2]\) \(4380672\) \(2.0061\) \(\Gamma_0(N)\)-optimal
407330.f2 407330f2 \([1, -1, 0, 434210, -133461534]\) \(5026574097/7174090\) \(-12921631297075093670\) \([2]\) \(8761344\) \(2.3527\)  

Rank

sage: E.rank()
 

The elliptic curves in class 407330.f have rank \(0\).

Complex multiplication

The elliptic curves in class 407330.f do not have complex multiplication.

Modular form 407330.2.a.f

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