Properties

Label 348480cp
Number of curves $4$
Conductor $348480$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348480cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348480.cp4 348480cp1 \([0, 0, 0, 952512, -1314697912]\) \(72268906496/606436875\) \(-801990450465747840000\) \([2]\) \(8847360\) \(2.6925\) \(\Gamma_0(N)\)-optimal
348480.cp3 348480cp2 \([0, 0, 0, -13748988, -18068527312]\) \(13584145739344/1195803675\) \(25302501678694171852800\) \([2]\) \(17694720\) \(3.0391\)  
348480.cp2 348480cp3 \([0, 0, 0, -68046528, -216222557848]\) \(-26348629355659264/24169921875\) \(-31963832232750000000000\) \([2]\) \(26542080\) \(3.2418\)  
348480.cp1 348480cp4 \([0, 0, 0, -1088984028, -13831853432848]\) \(6749703004355978704/5671875\) \(120013535423232000000\) \([2]\) \(53084160\) \(3.5884\)  

Rank

sage: E.rank()
 

The elliptic curves in class 348480cp have rank \(1\).

Complex multiplication

The elliptic curves in class 348480cp do not have complex multiplication.

Modular form 348480.2.a.cp

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{7} + 2q^{13} + 2q^{19} + O(q^{20})\)  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 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.