Properties

Label 7220.b
Number of curves $2$
Conductor $7220$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7220.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7220.b1 7220d1 \([0, 1, 0, -332601, -68967860]\) \(5405726654464/407253125\) \(306553312890050000\) \([2]\) \(86400\) \(2.1006\) \(\Gamma_0(N)\)-optimal
7220.b2 7220d2 \([0, 1, 0, 319004, -305630796]\) \(298091207216/3525390625\) \(-42458907602500000000\) \([2]\) \(172800\) \(2.4472\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7220.b have rank \(1\).

Complex multiplication

The elliptic curves in class 7220.b do not have complex multiplication.

Modular form 7220.2.a.b

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