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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 336336bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336336.bj2 | 336336bj1 | \([0, -1, 0, -1160336, 481470144]\) | \(860833894093732321/8282804244\) | \(1662391942987776\) | \([]\) | \(3838464\) | \(2.0821\) | \(\Gamma_0(N)\)-optimal |
336336.bj1 | 336336bj2 | \([0, -1, 0, -37400176, -87999230528]\) | \(28826282175168869972161/9077387406557184\) | \(1821867962045653057536\) | \([]\) | \(26869248\) | \(3.0551\) |
Rank
sage: E.rank()
The elliptic curves in class 336336bj have rank \(1\).
Complex multiplication
The elliptic curves in class 336336bj do not have complex multiplication.Modular form 336336.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.