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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3465.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3465.n1 | 3465i5 | \([1, -1, 0, -27442800, 55340692911]\) | \(3135316978843283198764801/571725\) | \(416787525\) | \([2]\) | \(61440\) | \(2.4484\) | |
| 3465.n2 | 3465i4 | \([1, -1, 0, -1715175, 865019736]\) | \(765458482133960722801/326869475625\) | \(238287847730625\) | \([2, 2]\) | \(30720\) | \(2.1019\) | |
| 3465.n3 | 3465i6 | \([1, -1, 0, -1706670, 874016325]\) | \(-754127868744065783521/15825714261328125\) | \(-11536945696508203125\) | \([2]\) | \(61440\) | \(2.4484\) | |
| 3465.n4 | 3465i3 | \([1, -1, 0, -229005, -22186710]\) | \(1821931919215868881/761147600816295\) | \(554876600995079055\) | \([2]\) | \(30720\) | \(2.1019\) | |
| 3465.n5 | 3465i2 | \([1, -1, 0, -107730, 13395375]\) | \(189674274234120481/3859869269025\) | \(2813844697119225\) | \([2, 2]\) | \(15360\) | \(1.7553\) | |
| 3465.n6 | 3465i1 | \([1, -1, 0, 315, 624456]\) | \(4733169839/231139696095\) | \(-168500838453255\) | \([2]\) | \(7680\) | \(1.4087\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3465.n have rank \(0\).
Complex multiplication
The elliptic curves in class 3465.n do not have complex multiplication.Modular form 3465.2.a.n
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
