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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 119952.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.be1 | 119952fi2 | \([0, 0, 0, -15771, 760970]\) | \(423564751/867\) | \(887974907904\) | \([2]\) | \(262144\) | \(1.1790\) | |
119952.be2 | 119952fi1 | \([0, 0, 0, -651, 20090]\) | \(-29791/153\) | \(-156701454336\) | \([2]\) | \(131072\) | \(0.83243\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.be have rank \(2\).
Complex multiplication
The elliptic curves in class 119952.be do not have complex multiplication.Modular form 119952.2.a.be
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.