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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 202800.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.n1 | 202800je4 | \([0, -1, 0, -35153408, -80211350688]\) | \(31103978031362/195\) | \(30119288160000000\) | \([2]\) | \(12386304\) | \(2.7676\) | |
202800.n2 | 202800je3 | \([0, -1, 0, -3043408, -199990688]\) | \(20183398562/11567205\) | \(1786646054363040000000\) | \([2]\) | \(12386304\) | \(2.7676\) | |
202800.n3 | 202800je2 | \([0, -1, 0, -2198408, -1251170688]\) | \(15214885924/38025\) | \(2936630595600000000\) | \([2, 2]\) | \(6193152\) | \(2.4210\) | |
202800.n4 | 202800je1 | \([0, -1, 0, -85908, -34370688]\) | \(-3631696/24375\) | \(-470613877500000000\) | \([2]\) | \(3096576\) | \(2.0744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.n have rank \(1\).
Complex multiplication
The elliptic curves in class 202800.n do not have complex multiplication.Modular form 202800.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.