Properties

Label 103488ff
Number of curves $4$
Conductor $103488$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ff1")
 
E.isogeny_class()
 

Elliptic curves in class 103488ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103488.ca3 103488ff1 \([0, -1, 0, -17313, 832833]\) \(18609625/1188\) \(36639083593728\) \([2]\) \(276480\) \(1.3533\) \(\Gamma_0(N)\)-optimal
103488.ca4 103488ff2 \([0, -1, 0, 14047, 3485889]\) \(9938375/176418\) \(-5440903913668608\) \([2]\) \(552960\) \(1.6999\)  
103488.ca1 103488ff3 \([0, -1, 0, -252513, -48568575]\) \(57736239625/255552\) \(7881473981939712\) \([2]\) \(829440\) \(1.9026\)  
103488.ca2 103488ff4 \([0, -1, 0, -127073, -96963327]\) \(-7357983625/127552392\) \(-3933840701235658752\) \([2]\) \(1658880\) \(2.2492\)  

Rank

sage: E.rank()
 

The elliptic curves in class 103488ff have rank \(1\).

Complex multiplication

The elliptic curves in class 103488ff do not have complex multiplication.

Modular form 103488.2.a.ff

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