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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 110670a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110670.d4 | 110670a1 | \([1, 1, 0, -2005633, 86874613]\) | \(892233346660440794027929/513015324982609182720\) | \(513015324982609182720\) | \([2]\) | \(6578176\) | \(2.6635\) | \(\Gamma_0(N)\)-optimal |
| 110670.d2 | 110670a2 | \([1, 1, 0, -22977153, 42285767157]\) | \(1341567071464214185939392409/3566818114559646105600\) | \(3566818114559646105600\) | \([2, 2]\) | \(13156352\) | \(3.0101\) | |
| 110670.d3 | 110670a3 | \([1, 1, 0, -14099073, 75331756533]\) | \(-309952709923399776210900889/2272556962862968508160000\) | \(-2272556962862968508160000\) | \([2]\) | \(26312704\) | \(3.3567\) | |
| 110670.d1 | 110670a4 | \([1, 1, 0, -367399553, 2710388330997]\) | \(5484532125809566566005365594009/38922235338282670080\) | \(38922235338282670080\) | \([2]\) | \(26312704\) | \(3.3567\) |
Rank
sage: E.rank()
The elliptic curves in class 110670a have rank \(0\).
Complex multiplication
The elliptic curves in class 110670a do not have complex multiplication.Modular form 110670.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
