Properties

Label 35301.c
Number of curves $6$
Conductor $35301$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 35301.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35301.c1 35301e6 \([1, 1, 1, -1317939, -582908538]\) \(53297461115137/147\) \(698265323427\) \([2]\) \(281600\) \(1.9310\)  
35301.c2 35301e4 \([1, 1, 1, -82404, -9126084]\) \(13027640977/21609\) \(102645002543769\) \([2, 2]\) \(140800\) \(1.5844\)  
35301.c3 35301e3 \([1, 1, 1, -65594, 6399632]\) \(6570725617/45927\) \(218158037476407\) \([2]\) \(140800\) \(1.5844\)  
35301.c4 35301e5 \([1, 1, 1, -57189, -14784330]\) \(-4354703137/17294403\) \(-82150217035863123\) \([2]\) \(281600\) \(1.9310\)  
35301.c5 35301e2 \([1, 1, 1, -6759, -48684]\) \(7189057/3969\) \(18853163732529\) \([2, 2]\) \(70400\) \(1.2378\)  
35301.c6 35301e1 \([1, 1, 1, 1646, -4978]\) \(103823/63\) \(-299256567183\) \([2]\) \(35200\) \(0.89127\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35301.c have rank \(0\).

Complex multiplication

The elliptic curves in class 35301.c do not have complex multiplication.

Modular form 35301.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 2 q^{13} - q^{14} + 2 q^{15} - q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.