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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 260100l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
260100.l1 | 260100l1 | \([0, 0, 0, -1820700, -945138375]\) | \(151732224/85\) | \(373921115771250000\) | \([2]\) | \(5308416\) | \(2.3191\) | \(\Gamma_0(N)\)-optimal |
260100.l2 | 260100l2 | \([0, 0, 0, -1495575, -1293347250]\) | \(-5256144/7225\) | \(-508532717448900000000\) | \([2]\) | \(10616832\) | \(2.6657\) |
Rank
sage: E.rank()
The elliptic curves in class 260100l have rank \(1\).
Complex multiplication
The elliptic curves in class 260100l do not have complex multiplication.Modular form 260100.2.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.