Properties

Label 76440l
Number of curves $4$
Conductor $76440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 76440l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76440.q3 76440l1 \([0, -1, 0, -53916, -4223820]\) \(575514878416/74972625\) \(2258036315808000\) \([2]\) \(442368\) \(1.6745\) \(\Gamma_0(N)\)-optimal
76440.q2 76440l2 \([0, -1, 0, -219536, 35326236]\) \(9713030100484/1164515625\) \(140292197136000000\) \([2, 2]\) \(884736\) \(2.0210\)  
76440.q4 76440l3 \([0, -1, 0, 315544, 180225900]\) \(14420619677518/66650390625\) \(-16059088500000000000\) \([2]\) \(1769472\) \(2.3676\)  
76440.q1 76440l4 \([0, -1, 0, -3404536, 2418980236]\) \(18112543427820242/316031625\) \(76146287922432000\) \([2]\) \(1769472\) \(2.3676\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76440l have rank \(1\).

Complex multiplication

The elliptic curves in class 76440l do not have complex multiplication.

Modular form 76440.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.