Properties

Label 370881r
Number of curves $2$
Conductor $370881$
CM \(\Q(\sqrt{-3}) \)
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 370881r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
370881.r1 370881r1 \([0, 0, 1, 0, -1237742]\) \(0\) \(-661826004347403\) \([]\) \(1064880\) \(1.5227\) \(\Gamma_0(N)\)-optimal \(-3\)
370881.r2 370881r2 \([0, 0, 1, 0, 33419027]\) \(0\) \(-482471157169256787\) \([]\) \(3194640\) \(2.0720\)   \(-3\)

Rank

sage: E.rank()
 

The elliptic curves in class 370881r have rank \(1\).

Complex multiplication

Each elliptic curve in class 370881r has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 370881.2.a.r

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 5 q^{13} + 4 q^{16} - 8 q^{19} + O(q^{20})\) 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 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.