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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 233450.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
233450.bs1 | 233450bs2 | \([1, 0, 0, -4327778538, 109583259250192]\) | \(573718392227901342193352375257/22016176259779893044\) | \(344002754059060828812500\) | \([2]\) | \(186253312\) | \(4.0073\) | |
233450.bs2 | 233450bs1 | \([1, 0, 0, -270084038, 1717566356692]\) | \(-139444195316122186685933977/867810592237096964848\) | \(-13559540503704640075750000\) | \([2]\) | \(93126656\) | \(3.6607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 233450.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 233450.bs do not have complex multiplication.Modular form 233450.2.a.bs
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.