Properties

Label 30420j
Number of curves 4
Conductor 30420
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("30420.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30420j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30420.c3 30420j1 [0, 0, 0, -2028, -24167] [2] 27648 \(\Gamma_0(N)\)-optimal
30420.c4 30420j2 [0, 0, 0, 5577, -162578] [2] 55296  
30420.c1 30420j3 [0, 0, 0, -62868, 6065917] [2] 82944  
30420.c2 30420j4 [0, 0, 0, -55263, 7588438] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 30420j have rank \(1\).

Modular form 30420.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{5} - 2q^{7} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.