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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 271440b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.b1 | 271440b1 | \([0, 0, 0, -274323, -53955502]\) | \(764579942079121/21285239040\) | \(63557383209615360\) | \([2]\) | \(2654208\) | \(2.0035\) | \(\Gamma_0(N)\)-optimal |
271440.b2 | 271440b2 | \([0, 0, 0, 59757, -176963758]\) | \(7903193128559/4535269736400\) | \(-13542242868574617600\) | \([2]\) | \(5308416\) | \(2.3501\) |
Rank
sage: E.rank()
The elliptic curves in class 271440b have rank \(0\).
Complex multiplication
The elliptic curves in class 271440b do not have complex multiplication.Modular form 271440.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.