Properties

Label 310464.ie
Number of curves $2$
Conductor $310464$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ie1")
 
E.isogeny_class()
 

Elliptic curves in class 310464.ie

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.ie1 310464ie1 \([0, 0, 0, -9975, -382984]\) \(6859000000/9801\) \(156845481408\) \([2]\) \(327680\) \(1.0510\) \(\Gamma_0(N)\)-optimal
310464.ie2 310464ie2 \([0, 0, 0, -7140, -605248]\) \(-39304000/131769\) \(-134956823113728\) \([2]\) \(655360\) \(1.3975\)  

Rank

sage: E.rank()
 

The elliptic curves in class 310464.ie have rank \(0\).

Complex multiplication

The elliptic curves in class 310464.ie do not have complex multiplication.

Modular form 310464.2.a.ie

sage: E.q_eigenform(10)
 
\(q - q^{11} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.