Properties

Label 352800.mg
Number of curves $4$
Conductor $352800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("mg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 352800.mg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.mg1 352800mg2 \([0, 0, 0, -1125211503675, 459408851879773250]\) \(229625675762164624948320008/9568125\) \(6564967731945000000000\) \([2]\) \(1981808640\) \(5.0870\)  
352800.mg2 352800mg4 \([0, 0, 0, -70566894300, 7126549533992000]\) \(7079962908642659949376/100085966990454375\) \(549375049939540209358680000000000\) \([2]\) \(1981808640\) \(5.0870\)  
352800.mg3 352800mg1 \([0, 0, 0, -70325722425, 7178262572117000]\) \(448487713888272974160064/91549016015625\) \(7851803985027031640625000000\) \([2, 2]\) \(990904320\) \(4.7404\) \(\Gamma_0(N)\)-optimal
352800.mg4 352800mg3 \([0, 0, 0, -70084605675, 7229928345956750]\) \(-55486311952875723077768/801237030029296875\) \(-549751936537386474609375000000000\) \([2]\) \(1981808640\) \(5.0870\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800.mg have rank \(0\).

Complex multiplication

The elliptic curves in class 352800.mg do not have complex multiplication.

Modular form 352800.2.a.mg

sage: E.q_eigenform(10)
 
\(q + 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.