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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3366.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3366.b1 | 3366b2 | \([1, -1, 0, -9972963, -8638649195]\) | \(150476552140919246594353/42832838728685592576\) | \(31225139433211796987904\) | \([2]\) | \(259584\) | \(3.0230\) | |
3366.b2 | 3366b1 | \([1, -1, 0, -3706083, 2640481429]\) | \(7722211175253055152433/340131399900069888\) | \(247955790527150948352\) | \([2]\) | \(129792\) | \(2.6764\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3366.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3366.b do not have complex multiplication.Modular form 3366.2.a.b
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.