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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 393129bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
393129.bx1 | 393129bx1 | \([0, 0, 1, -10745526, -15855362141]\) | \(-2258403328/480491\) | \(-29193791524702109593299\) | \([]\) | \(31104000\) | \(3.0321\) | \(\Gamma_0(N)\)-optimal |
393129.bx2 | 393129bx2 | \([0, 0, 1, 75742854, 91697262808]\) | \(790939860992/517504691\) | \(-31442678556121517556267099\) | \([]\) | \(93312000\) | \(3.5814\) |
Rank
sage: E.rank()
The elliptic curves in class 393129bx have rank \(0\).
Complex multiplication
The elliptic curves in class 393129bx do not have complex multiplication.Modular form 393129.2.a.bx
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.