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Properties

Label 454400m
Number of curves $3$
Conductor $454400$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 454400m have rank \(1\).

Complex multiplication

The elliptic curves in class 454400m do not have complex multiplication.

Modular form 454400.2.a.m

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{7} - 2 q^{9} + q^{13} + 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 454400m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
454400.m3 454400m1 \([0, -1, 0, -95933, -11404763]\) \(190705121216/71\) \(36352000000\) \([]\) \(753664\) \(1.3778\) \(\Gamma_0(N)\)-optimal*
454400.m2 454400m2 \([0, -1, 0, -431933, 99139237]\) \(17406197775296/1804229351\) \(923765427712000000\) \([]\) \(3768320\) \(2.1825\) \(\Gamma_0(N)\)-optimal*
454400.m1 454400m3 \([0, -1, 0, -262847933, 1640318419237]\) \(3922540634246430781376/71\) \(36352000000\) \([]\) \(18841600\) \(2.9872\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 454400m1.