Properties

Label 370300.d
Number of curves $2$
Conductor $370300$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 370300.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370300.d1 370300d2 \([0, 1, 0, -1961708, 695005588]\) \(11279504/3703\) \(274088448483500000000\) \([2]\) \(15206400\) \(2.6247\)  
370300.d2 370300d1 \([0, 1, 0, 352667, 74753088]\) \(1048576/1127\) \(-5213638965718750000\) \([2]\) \(7603200\) \(2.2781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 370300.d have rank \(0\).

Complex multiplication

The elliptic curves in class 370300.d do not have complex multiplication.

Modular form 370300.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} - 2 q^{11} - 6 q^{13} + 6 q^{17} + O(q^{20})\) 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.