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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 157200be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157200.cz2 | 157200be1 | \([0, 1, 0, -15808, -769612]\) | \(6826561273/7074\) | \(452736000000\) | \([]\) | \(393984\) | \(1.1543\) | \(\Gamma_0(N)\)-optimal |
157200.cz1 | 157200be2 | \([0, 1, 0, -57808, 4522388]\) | \(333822098953/53954184\) | \(3453067776000000\) | \([]\) | \(1181952\) | \(1.7036\) |
Rank
sage: E.rank()
The elliptic curves in class 157200be have rank \(0\).
Complex multiplication
The elliptic curves in class 157200be do not have complex multiplication.Modular form 157200.2.a.be
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.