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Properties

Label 416025t
Number of curves $2$
Conductor $416025$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 416025t have rank \(1\).

Complex multiplication

The elliptic curves in class 416025t do not have complex multiplication.

Modular form 416025.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 4 q^{7} + 3 q^{8} + 2 q^{11} - 2 q^{13} - 4 q^{14} - q^{16} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 416025t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416025.t1 416025t1 \([1, -1, 1, -9369230, 10819331772]\) \(1263214441/29025\) \(2089924110319953515625\) \([2]\) \(25546752\) \(2.8773\) \(\Gamma_0(N)\)-optimal
416025.t2 416025t2 \([1, -1, 1, 1031395, 33513495522]\) \(1685159/6739605\) \(-485280378416293206328125\) \([2]\) \(51093504\) \(3.2239\)