Properties

Label 2450.t
Number of curves $6$
Conductor $2450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2450.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.t1 2450y6 \([1, 0, 0, -3344888, 2354339392]\) \(2251439055699625/25088\) \(46118408000000\) \([2]\) \(41472\) \(2.1908\)  
2450.t2 2450y5 \([1, 0, 0, -208888, 36835392]\) \(-548347731625/1835008\) \(-3373232128000000\) \([2]\) \(20736\) \(1.8442\)  
2450.t3 2450y4 \([1, 0, 0, -43513, 2860017]\) \(4956477625/941192\) \(1730160900125000\) \([2]\) \(13824\) \(1.6415\)  
2450.t4 2450y2 \([1, 0, 0, -12888, -563858]\) \(128787625/98\) \(180150031250\) \([2]\) \(4608\) \(1.0922\)  
2450.t5 2450y1 \([1, 0, 0, -638, -12608]\) \(-15625/28\) \(-51471437500\) \([2]\) \(2304\) \(0.74559\) \(\Gamma_0(N)\)-optimal
2450.t6 2450y3 \([1, 0, 0, 5487, 263017]\) \(9938375/21952\) \(-40353607000000\) \([2]\) \(6912\) \(1.2949\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2450.t have rank \(1\).

Complex multiplication

The elliptic curves in class 2450.t do not have complex multiplication.

Modular form 2450.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + q^{8} + q^{9} - 2 q^{12} - 4 q^{13} + q^{16} + 6 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.