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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 76440.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.bj1 | 76440ch2 | \([0, -1, 0, -328400, -72326148]\) | \(11151682683009628/40040325\) | \(14063443430400\) | \([2]\) | \(479232\) | \(1.7406\) | |
76440.bj2 | 76440ch1 | \([0, -1, 0, -20820, -1090620]\) | \(11367178023472/651619215\) | \(57217380030720\) | \([2]\) | \(239616\) | \(1.3940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76440.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 76440.bj do not have complex multiplication.Modular form 76440.2.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 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.