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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28314.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.b1 | 28314w1 | \([1, -1, 0, -113241321, 463855087053]\) | \(-124352595912593543977/103332962304\) | \(-133451210957500440576\) | \([]\) | \(2995200\) | \(3.1650\) | \(\Gamma_0(N)\)-optimal |
| 28314.b2 | 28314w2 | \([1, -1, 0, -87905736, 676853506368]\) | \(-58169016237585194137/119573538788081664\) | \(-154425395284786548012220416\) | \([]\) | \(8985600\) | \(3.7143\) |
Rank
sage: E.rank()
The elliptic curves in class 28314.b have rank \(1\).
Complex multiplication
The elliptic curves in class 28314.b do not have complex multiplication.Modular form 28314.2.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 LMFDB 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 LMFDB labels.
