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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 238260.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238260.t1 | 238260t2 | \([0, 1, 0, -27556, -1755436]\) | \(192143824/1815\) | \(21859398147840\) | \([2]\) | \(684288\) | \(1.3804\) | |
238260.t2 | 238260t1 | \([0, 1, 0, -481, -65956]\) | \(-16384/2475\) | \(-1863016887600\) | \([2]\) | \(342144\) | \(1.0338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238260.t have rank \(1\).
Complex multiplication
The elliptic curves in class 238260.t do not have complex multiplication.Modular form 238260.2.a.t
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.