Properties

Label 3120h
Number of curves $4$
Conductor $3120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 3120h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.p4 3120h1 \([0, 1, 0, 84, -180]\) \(253012016/219375\) \(-56160000\) \([2]\) \(768\) \(0.17451\) \(\Gamma_0(N)\)-optimal
3120.p3 3120h2 \([0, 1, 0, -416, -1980]\) \(7793764996/3080025\) \(3153945600\) \([2, 2]\) \(1536\) \(0.52108\)  
3120.p1 3120h3 \([0, 1, 0, -5816, -172620]\) \(10625310339698/3855735\) \(7896545280\) \([2]\) \(3072\) \(0.86766\)  
3120.p2 3120h4 \([0, 1, 0, -3016, 61460]\) \(1481943889298/34543665\) \(70745425920\) \([2]\) \(3072\) \(0.86766\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3120h have rank \(1\).

Complex multiplication

The elliptic curves in class 3120h do not have complex multiplication.

Modular form 3120.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.