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Properties

Label 357378.l
Number of curves $3$
Conductor $357378$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 357378.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
357378.l1 357378l3 \([1, 0, 0, -193149169647, -32672893402475361]\) \(-796897103803836591798258764661693006193/325708012029457050422660406\) \(-325708012029457050422660406\) \([]\) \(1955912832\) \(4.8701\)  
357378.l2 357378l2 \([1, 0, 0, -2342114817, -46491207963039]\) \(-1420850082701996138362832375655313/111479759347929068314392183576\) \(-111479759347929068314392183576\) \([3]\) \(651970944\) \(4.3208\)  
357378.l3 357378l1 \([1, 0, 0, 168357063, -28208561031]\) \(527737231583370421518916605167/305747584820092901684491776\) \(-305747584820092901684491776\) \([9]\) \(217323648\) \(3.7715\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 357378.l have rank \(0\).

Complex multiplication

The elliptic curves in class 357378.l do not have complex multiplication.

Modular form 357378.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - 4 q^{13} + q^{14} - 3 q^{15} + q^{16} + q^{18} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.