Properties

Label 3150k
Number of curves $8$
Conductor $3150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.f7 3150k1 \([1, -1, 0, -111942, -14382284]\) \(13619385906841/6048000\) \(68890500000000\) \([2]\) \(18432\) \(1.6138\) \(\Gamma_0(N)\)-optimal
3150.f6 3150k2 \([1, -1, 0, -129942, -9432284]\) \(21302308926361/8930250000\) \(101721128906250000\) \([2, 2]\) \(36864\) \(1.9604\)  
3150.f5 3150k3 \([1, -1, 0, -331317, 55868341]\) \(353108405631241/86318776320\) \(983224811520000000\) \([2]\) \(55296\) \(2.1631\)  
3150.f4 3150k4 \([1, -1, 0, -980442, 367339216]\) \(9150443179640281/184570312500\) \(2102371215820312500\) \([2]\) \(73728\) \(2.3070\)  
3150.f8 3150k5 \([1, -1, 0, 432558, -69619784]\) \(785793873833639/637994920500\) \(-7267160891320312500\) \([2]\) \(73728\) \(2.3070\)  
3150.f2 3150k6 \([1, -1, 0, -4939317, 4226108341]\) \(1169975873419524361/108425318400\) \(1235032142400000000\) \([2, 2]\) \(110592\) \(2.5097\)  
3150.f1 3150k7 \([1, -1, 0, -79027317, 270424292341]\) \(4791901410190533590281/41160000\) \(468838125000000\) \([2]\) \(221184\) \(2.8563\)  
3150.f3 3150k8 \([1, -1, 0, -4579317, 4867988341]\) \(-932348627918877961/358766164249920\) \(-4086570839659245000000\) \([2]\) \(221184\) \(2.8563\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3150k have rank \(0\).

Complex multiplication

The elliptic curves in class 3150k do not have complex multiplication.

Modular form 3150.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 2q^{13} + q^{14} + q^{16} - 6q^{17} + 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.