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Properties

Label 35378o
Number of curves $3$
Conductor $35378$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 35378o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.n2 35378o1 \([1, 0, 0, -274548, 55364840]\) \(-413493625/152\) \(-841304929772888\) \([]\) \(272160\) \(1.8317\) \(\Gamma_0(N)\)-optimal
35378.n3 35378o2 \([1, 0, 0, 167677, 210479681]\) \(94196375/3511808\) \(-19437509097472804352\) \([]\) \(816480\) \(2.3810\)  
35378.n1 35378o3 \([1, 0, 0, -1512778, -5760849116]\) \(-69173457625/2550136832\) \(-14114754528664572919808\) \([]\) \(2449440\) \(2.9303\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35378o have rank \(0\).

Complex multiplication

The elliptic curves in class 35378o do not have complex multiplication.

Modular form 35378.2.a.o

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.