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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 30096bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30096.o2 | 30096bd1 | \([0, 0, 0, -52320, -4965712]\) | \(-5304438784000/497763387\) | \(-1486313509367808\) | \([]\) | \(103680\) | \(1.6533\) | \(\Gamma_0(N)\)-optimal |
30096.o1 | 30096bd2 | \([0, 0, 0, -4329120, -3466949776]\) | \(-3004935183806464000/2037123\) | \(-6082816684032\) | \([]\) | \(311040\) | \(2.2026\) |
Rank
sage: E.rank()
The elliptic curves in class 30096bd have rank \(0\).
Complex multiplication
The elliptic curves in class 30096bd do not have complex multiplication.Modular form 30096.2.a.bd
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.