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Properties

Label 35378.p
Number of curves $2$
Conductor $35378$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 35378.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.p1 35378j1 \([1, 1, 1, -26902, -1715393]\) \(-19061833/76\) \(-8584744181356\) \([]\) \(155520\) \(1.3388\) \(\Gamma_0(N)\)-optimal
35378.p2 35378j2 \([1, 1, 1, 61543, -8932505]\) \(228215687/438976\) \(-49585482391512256\) \([]\) \(466560\) \(1.8881\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35378.p have rank \(1\).

Complex multiplication

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

Modular form 35378.2.a.p

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