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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 74382.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74382.bj1 | 74382bg2 | \([1, 1, 1, -802621, -87930109]\) | \(486034459476995521/253095136942032\) | \(29776389766093122768\) | \([2]\) | \(2654208\) | \(2.4286\) | |
74382.bj2 | 74382bg1 | \([1, 1, 1, 189139, -10572829]\) | \(6360314548472639/4097346156288\) | \(-482048677941126912\) | \([2]\) | \(1327104\) | \(2.0820\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74382.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 74382.bj do not have complex multiplication.Modular form 74382.2.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.