Properties

Label 310464m
Number of curves $2$
Conductor $310464$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 310464m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.m2 310464m1 \([0, 0, 0, 24108, 2030560]\) \(4410944/7623\) \(-2677944895008768\) \([2]\) \(1966080\) \(1.6452\) \(\Gamma_0(N)\)-optimal
310464.m1 310464m2 \([0, 0, 0, -169932, 21046480]\) \(193100552/43659\) \(122698566098583552\) \([2]\) \(3932160\) \(1.9918\)  

Rank

sage: E.rank()
 

The elliptic curves in class 310464m have rank \(1\).

Complex multiplication

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

Modular form 310464.2.a.m

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - q^{11} + 6 q^{13} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.