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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 54150b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.h2 | 54150b1 | \([1, 1, 0, 13350, -1750500]\) | \(129205871/729000\) | \(-1484437640625000\) | \([]\) | \(311040\) | \(1.5932\) | \(\Gamma_0(N)\)-optimal |
54150.h1 | 54150b2 | \([1, 1, 0, -798900, -275478750]\) | \(-27692833539889/35156250\) | \(-71587463378906250\) | \([]\) | \(933120\) | \(2.1425\) |
Rank
sage: E.rank()
The elliptic curves in class 54150b have rank \(1\).
Complex multiplication
The elliptic curves in class 54150b do not have complex multiplication.Modular form 54150.2.a.b
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.