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SageMath
E = EllipticCurve("lk1")
E.isogeny_class()
Elliptic curves in class 286650lk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.lk2 | 286650lk1 | \([1, -1, 1, -98100680, -373959328053]\) | \(623295446073461/5458752\) | \(914406219806625000000\) | \([2]\) | \(35389440\) | \(3.1889\) | \(\Gamma_0(N)\)-optimal |
286650.lk1 | 286650lk2 | \([1, -1, 1, -100305680, -356266408053]\) | \(666276475992821/58199166792\) | \(9749056213245808265625000\) | \([2]\) | \(70778880\) | \(3.5355\) |
Rank
sage: E.rank()
The elliptic curves in class 286650lk have rank \(0\).
Complex multiplication
The elliptic curves in class 286650lk do not have complex multiplication.Modular form 286650.2.a.lk
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.