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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 323400.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
323400.bk1 | 323400bk2 | \([0, -1, 0, -344528, -76584948]\) | \(51506786656582/864536409\) | \(75913213001472000\) | \([2]\) | \(3194880\) | \(2.0372\) | |
323400.bk2 | 323400bk1 | \([0, -1, 0, -343128, -77248548]\) | \(101762874214124/29403\) | \(1290909312000\) | \([2]\) | \(1597440\) | \(1.6906\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 323400.bk do not have complex multiplication.Modular form 323400.2.a.bk
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.