Properties

Label 7220.f
Number of curves $4$
Conductor $7220$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7220.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7220.f1 7220c3 \([0, -1, 0, -14921, 706370]\) \(488095744/125\) \(94091762000\) \([2]\) \(10368\) \(1.0916\)  
7220.f2 7220c4 \([0, -1, 0, -13116, 881816]\) \(-20720464/15625\) \(-188183524000000\) \([2]\) \(20736\) \(1.4381\)  
7220.f3 7220c1 \([0, -1, 0, -481, -2634]\) \(16384/5\) \(3763670480\) \([2]\) \(3456\) \(0.54227\) \(\Gamma_0(N)\)-optimal
7220.f4 7220c2 \([0, -1, 0, 1324, -19240]\) \(21296/25\) \(-301093638400\) \([2]\) \(6912\) \(0.88884\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7220.2.a.f

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.