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Properties

Label 35378n
Number of curves $2$
Conductor $35378$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 35378n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.o2 35378n1 \([1, 0, 0, 97, -799]\) \(2375/8\) \(-339770312\) \([]\) \(10368\) \(0.32005\) \(\Gamma_0(N)\)-optimal
35378.o1 35378n2 \([1, 0, 0, -4558, -119036]\) \(-246579625/512\) \(-21745299968\) \([]\) \(31104\) \(0.86936\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35378.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.