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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 54450db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.bj2 | 54450db1 | \([1, -1, 0, -218367, 20357541]\) | \(18865/8\) | \(488336325778125000\) | \([]\) | \(760320\) | \(2.0909\) | \(\Gamma_0(N)\)-optimal |
54450.bj1 | 54450db2 | \([1, -1, 0, -15192117, 22795431291]\) | \(6352571665/2\) | \(122084081444531250\) | \([3]\) | \(2280960\) | \(2.6402\) |
Rank
sage: E.rank()
The elliptic curves in class 54450db have rank \(0\).
Complex multiplication
The elliptic curves in class 54450db do not have complex multiplication.Modular form 54450.2.a.db
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.