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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1210.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1210.l1 | 1210l1 | \([1, 0, 0, -73510, -7801628]\) | \(-1693700041/32000\) | \(-829997587232000\) | \([]\) | \(6336\) | \(1.6573\) | \(\Gamma_0(N)\)-optimal |
1210.l2 | 1210l2 | \([1, 0, 0, 292515, -36424783]\) | \(106718863559/83886080\) | \(-2175788875073454080\) | \([]\) | \(19008\) | \(2.2066\) |
Rank
sage: E.rank()
The elliptic curves in class 1210.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1210.l do not have complex multiplication.Modular form 1210.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.