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SageMath
E = EllipticCurve("ie1")
E.isogeny_class()
Elliptic curves in class 310464.ie
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.ie1 | 310464ie1 | \([0, 0, 0, -9975, -382984]\) | \(6859000000/9801\) | \(156845481408\) | \([2]\) | \(327680\) | \(1.0510\) | \(\Gamma_0(N)\)-optimal |
310464.ie2 | 310464ie2 | \([0, 0, 0, -7140, -605248]\) | \(-39304000/131769\) | \(-134956823113728\) | \([2]\) | \(655360\) | \(1.3975\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.ie have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.ie do not have complex multiplication.Modular form 310464.2.a.ie
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.