Properties

Label 420.a
Number of curves $2$
Conductor $420$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 420.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
420.a1 420a1 \([0, -1, 0, -4061, 67590]\) \(463030539649024/149501953125\) \(2392031250000\) \([2]\) \(840\) \(1.0787\) \(\Gamma_0(N)\)-optimal
420.a2 420a2 \([0, -1, 0, 11564, 448840]\) \(667990736021936/732392128125\) \(-187492384800000\) \([2]\) \(1680\) \(1.4253\)  

Rank

sage: E.rank()
 

The elliptic curves in class 420.a have rank \(0\).

Complex multiplication

The elliptic curves in class 420.a do not have complex multiplication.

Modular form 420.2.a.a

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.