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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 282534bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
282534.bc2 | 282534bc1 | \([1, 0, 1, 1105610, -548704600]\) | \(596183/864\) | \(-216602919312962315616\) | \([]\) | \(12889800\) | \(2.5876\) | \(\Gamma_0(N)\)-optimal |
282534.bc1 | 282534bc2 | \([1, 0, 1, -33504805, -75030317680]\) | \(-16591834777/98304\) | \(-24644598819608156798976\) | \([]\) | \(38669400\) | \(3.1369\) |
Rank
sage: E.rank()
The elliptic curves in class 282534bc have rank \(0\).
Complex multiplication
The elliptic curves in class 282534bc do not have complex multiplication.Modular form 282534.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.