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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 478800.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
478800.bb1 | 478800bb4 | \([0, 0, 0, -45158427075, -3693654956722750]\) | \(218289391029690300712901881/306514992000\) | \(14300763466752000000000\) | \([2]\) | \(495452160\) | \(4.4161\) | |
478800.bb2 | 478800bb3 | \([0, 0, 0, -2953755075, -52046647474750]\) | \(61085713691774408830201/10268551781250000000\) | \(479089551906000000000000000000\) | \([2]\) | \(495452160\) | \(4.4161\) | \(\Gamma_0(N)\)-optimal* |
478800.bb3 | 478800bb2 | \([0, 0, 0, -2822427075, -57712268722750]\) | \(53294746224000958661881/1997017344000000\) | \(93172841201664000000000000\) | \([2, 2]\) | \(247726080\) | \(4.0695\) | \(\Gamma_0(N)\)-optimal* |
478800.bb4 | 478800bb1 | \([0, 0, 0, -168219075, -989189554750]\) | \(-11283450590382195961/2530373271552000\) | \(-118057095357530112000000000\) | \([2]\) | \(123863040\) | \(3.7230\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 478800.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 478800.bb do not have complex multiplication.Modular form 478800.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.