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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 88935m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88935.bq6 | 88935m1 | \([1, 1, 0, 207392, -10559939837]\) | \(4733169839/231139696095\) | \(-48174685593168039052455\) | \([2]\) | \(5529600\) | \(3.0313\) | \(\Gamma_0(N)\)-optimal |
| 88935.bq5 | 88935m2 | \([1, 1, 0, -70970253, -226071613368]\) | \(189674274234120481/3859869269025\) | \(804483139882579144443225\) | \([2, 2]\) | \(11059200\) | \(3.3779\) | |
| 88935.bq4 | 88935m3 | \([1, 1, 0, -150863528, 376052042997]\) | \(1821931919215868881/761147600816295\) | \(158640194561164283154750255\) | \([2]\) | \(22118400\) | \(3.7245\) | |
| 88935.bq2 | 88935m4 | \([1, 1, 0, -1129919298, -14619518822817]\) | \(765458482133960722801/326869475625\) | \(68126914088205870830625\) | \([2, 2]\) | \(22118400\) | \(3.7245\) | |
| 88935.bq3 | 88935m5 | \([1, 1, 0, -1124316393, -14771672431578]\) | \(-754127868744065783521/15825714261328125\) | \(-3298433032954438342695703125\) | \([2]\) | \(44236800\) | \(4.0710\) | |
| 88935.bq1 | 88935m6 | \([1, 1, 0, -18078706923, -935626807637892]\) | \(3135316978843283198764801/571725\) | \(119160285256383525\) | \([2]\) | \(44236800\) | \(4.0710\) |
Rank
sage: E.rank()
The elliptic curves in class 88935m have rank \(1\).
Complex multiplication
The elliptic curves in class 88935m do not have complex multiplication.Modular form 88935.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
