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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 101568l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101568.n2 | 101568l1 | \([0, -1, 0, -15752209, -24142001135]\) | \(-14647977776/59049\) | \(-1742541021294242807808\) | \([2]\) | \(8478720\) | \(2.9324\) | \(\Gamma_0(N)\)-optimal |
101568.n1 | 101568l2 | \([0, -1, 0, -252278689, -1542216255071]\) | \(15043017316604/243\) | \(28683802819658317824\) | \([2]\) | \(16957440\) | \(3.2790\) |
Rank
sage: E.rank()
The elliptic curves in class 101568l have rank \(0\).
Complex multiplication
The elliptic curves in class 101568l do not have complex multiplication.Modular form 101568.2.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 Cremona 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 Cremona labels.