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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 223440.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
223440.fl1 | 223440b4 | \([0, 1, 0, -363173120, 1700907890100]\) | \(10993009831928446009969/3767761230468750000\) | \(1815647604750000000000000000\) | \([2]\) | \(149299200\) | \(3.9325\) | |
223440.fl2 | 223440b2 | \([0, 1, 0, -325352960, 2258704221108]\) | \(7903870428425797297009/886464000000\) | \(427178406445056000000\) | \([2]\) | \(49766400\) | \(3.3832\) | |
223440.fl3 | 223440b1 | \([0, 1, 0, -20282880, 35475506100]\) | \(-1914980734749238129/20440940544000\) | \(-9850291052794085376000\) | \([2]\) | \(24883200\) | \(3.0366\) | \(\Gamma_0(N)\)-optimal |
223440.fl4 | 223440b3 | \([0, 1, 0, 67023360, 184723415988]\) | \(69096190760262356111/70568821500000000\) | \(-34006430845556736000000000\) | \([2]\) | \(74649600\) | \(3.5859\) |
Rank
sage: E.rank()
The elliptic curves in class 223440.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 223440.fl do not have complex multiplication.Modular form 223440.2.a.fl
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.