Properties

Label 397800.dh
Number of curves $2$
Conductor $397800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 397800.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.dh1 397800dh1 \([0, 0, 0, -82575, -9132750]\) \(21354132816/1105\) \(3222180000000\) \([2]\) \(1179648\) \(1.4692\) \(\Gamma_0(N)\)-optimal
397800.dh2 397800dh2 \([0, 0, 0, -78075, -10172250]\) \(-4512447684/1221025\) \(-14242035600000000\) \([2]\) \(2359296\) \(1.8158\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800.dh have rank \(0\).

Complex multiplication

The elliptic curves in class 397800.dh do not have complex multiplication.

Modular form 397800.2.a.dh

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - q^{13} + q^{17} + 2 q^{19} + O(q^{20})\) 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 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.