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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 101430br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.a4 | 101430br1 | \([1, -1, 0, -452475, 115926565]\) | \(119451676585249/1567702080\) | \(134455726285231680\) | \([2]\) | \(1327104\) | \(2.0943\) | \(\Gamma_0(N)\)-optimal |
101430.a3 | 101430br2 | \([1, -1, 0, -858195, -123529379]\) | \(815016062816929/394524156600\) | \(33836806552378548600\) | \([2]\) | \(2654208\) | \(2.4409\) | |
101430.a2 | 101430br3 | \([1, -1, 0, -3601215, -2570170919]\) | \(60221998378106209/1554376834500\) | \(133312871667323974500\) | \([2]\) | \(3981312\) | \(2.6436\) | |
101430.a1 | 101430br4 | \([1, -1, 0, -57257685, -166748237825]\) | \(242052349717010282689/167676468750\) | \(14380960307665218750\) | \([2]\) | \(7962624\) | \(2.9902\) |
Rank
sage: E.rank()
The elliptic curves in class 101430br have rank \(2\).
Complex multiplication
The elliptic curves in class 101430br do not have complex multiplication.Modular form 101430.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.