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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4998.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.l1 | 4998w2 | \([1, 0, 1, -2703552, -1711197554]\) | \(18575453384550358633/352517816448\) | \(41473368587290752\) | \([2]\) | \(129024\) | \(2.3123\) | |
4998.l2 | 4998w1 | \([1, 0, 1, -163392, -28595570]\) | \(-4100379159705193/626805817344\) | \(-73743077604704256\) | \([2]\) | \(64512\) | \(1.9658\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4998.l have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.l do not have complex multiplication.Modular form 4998.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.