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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3366.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3366.o1 | 3366l2 | \([1, -1, 1, -545, -4757]\) | \(661914925875/4114\) | \(111078\) | \([2]\) | \(1280\) | \(0.15443\) | |
3366.o2 | 3366l1 | \([1, -1, 1, -35, -65]\) | \(170953875/12716\) | \(343332\) | \([2]\) | \(640\) | \(-0.19214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3366.o have rank \(0\).
Complex multiplication
The elliptic curves in class 3366.o do not have complex multiplication.Modular form 3366.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.