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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 152592bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.c2 | 152592bj1 | \([0, -1, 0, -759877, 298862521]\) | \(-27172077568/5845851\) | \(-10439485084730186496\) | \([]\) | \(4230144\) | \(2.3705\) | \(\Gamma_0(N)\)-optimal |
152592.c1 | 152592bj2 | \([0, -1, 0, -64432357, 199090712329]\) | \(-16565495781326848/107811\) | \(-192528226680742656\) | \([]\) | \(12690432\) | \(2.9198\) |
Rank
sage: E.rank()
The elliptic curves in class 152592bj have rank \(0\).
Complex multiplication
The elliptic curves in class 152592bj do not have complex multiplication.Modular form 152592.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.