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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 105966l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
105966.o2 | 105966l1 | \([1, -1, 0, -2287257, -1437907411]\) | \(-3051779837625/295386112\) | \(-128087157577378987008\) | \([2]\) | \(3225600\) | \(2.5995\) | \(\Gamma_0(N)\)-optimal |
105966.o1 | 105966l2 | \([1, -1, 0, -37407417, -88051246003]\) | \(13350003080765625/109178272\) | \(47342559320087276448\) | \([2]\) | \(6451200\) | \(2.9460\) |
Rank
sage: E.rank()
The elliptic curves in class 105966l have rank \(0\).
Complex multiplication
The elliptic curves in class 105966l do not have complex multiplication.Modular form 105966.2.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.