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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 104742.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.t1 | 104742y4 | \([1, -1, 0, -237270800556, 44485157855631312]\) | \(13688695234222145601259673233/2003024259937536\) | \(216162698739138344921308416\) | \([2]\) | \(389283840\) | \(4.9039\) | |
104742.t2 | 104742y3 | \([1, -1, 0, -17042937516, 473972729682384]\) | \(5072972674420068408718993/2036482219218784389888\) | \(219773420245209566206510271324928\) | \([2]\) | \(389283840\) | \(4.9039\) | |
104742.t3 | 104742y2 | \([1, -1, 0, -14830786476, 694949363800272]\) | \(3342887139776073669969553/1278380674753560576\) | \(137960494137653569726180294656\) | \([2, 2]\) | \(194641920\) | \(4.5573\) | |
104742.t4 | 104742y1 | \([1, -1, 0, -790026156, 14177483380944]\) | \(-505304979693115442833/512169554353324032\) | \(-55272397491825116379812462592\) | \([2]\) | \(97320960\) | \(4.2107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 104742.t have rank \(0\).
Complex multiplication
The elliptic curves in class 104742.t do not have complex multiplication.Modular form 104742.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.