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Properties

Label 491985t
Number of curves $2$
Conductor $491985$
CM no
Rank $2$
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 491985t have rank \(2\).

Complex multiplication

The elliptic curves in class 491985t do not have complex multiplication.

Modular form 491985.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - q^{7} - 3 q^{11} + q^{13} + 4 q^{16} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 491985t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
491985.t2 491985t1 \([0, 0, 1, 10092, -506072]\) \(7077888/10985\) \(-176421622891995\) \([]\) \(1161216\) \(1.4189\) \(\Gamma_0(N)\)-optimal
491985.t1 491985t2 \([0, 0, 1, -317898, -69307441]\) \(-303464448/1625\) \(-19025349569269875\) \([]\) \(3483648\) \(1.9682\)