Properties

Label 331200ik
Number of curves $4$
Conductor $331200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ik1")
 
E.isogeny_class()
 

Elliptic curves in class 331200ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331200.ik4 331200ik1 \([0, 0, 0, -3560700, 16553194000]\) \(-26752376766544/618796614375\) \(-115482299361120000000000\) \([2]\) \(18874368\) \(3.1060\) \(\Gamma_0(N)\)-optimal
331200.ik3 331200ik2 \([0, 0, 0, -121658700, 514218166000]\) \(266763091319403556/1355769140625\) \(1012076240400000000000000\) \([2, 2]\) \(37748736\) \(3.4526\)  
331200.ik1 331200ik3 \([0, 0, 0, -1944158700, 32994813166000]\) \(544328872410114151778/14166950625\) \(21151143947520000000000\) \([2]\) \(75497472\) \(3.7992\)  
331200.ik2 331200ik4 \([0, 0, 0, -188726700, -115818626000]\) \(497927680189263938/284271240234375\) \(424414687500000000000000000\) \([2]\) \(75497472\) \(3.7992\)  

Rank

sage: E.rank()
 

The elliptic curves in class 331200ik have rank \(0\).

Complex multiplication

The elliptic curves in class 331200ik do not have complex multiplication.

Modular form 331200.2.a.ik

sage: E.q_eigenform(10)
 
\(q - 2 q^{13} - 6 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.