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Properties

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

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

Elliptic curves in class 35378.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.c1 35378g2 \([1, 1, 0, -1238598, -587844830]\) \(-37966934881/4952198\) \(-27409924938233134262\) \([]\) \(1188000\) \(2.4630\)  
35378.c2 35378g1 \([1, 1, 0, -368, 2790880]\) \(-1/608\) \(-3365219719091552\) \([]\) \(237600\) \(1.6582\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35378.2.a.c

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.