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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 152460bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.m2 | 152460bz1 | \([0, 0, 0, -33, 8437]\) | \(-76032/588245\) | \(-30748742640\) | \([]\) | \(103680\) | \(0.69134\) | \(\Gamma_0(N)\)-optimal |
152460.m1 | 152460bz2 | \([0, 0, 0, -32373, 2242053]\) | \(-98463644928/6125\) | \(-233401014000\) | \([]\) | \(311040\) | \(1.2406\) |
Rank
sage: E.rank()
The elliptic curves in class 152460bz have rank \(1\).
Complex multiplication
The elliptic curves in class 152460bz do not have complex multiplication.Modular form 152460.2.a.bz
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.