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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4368.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.j1 | 4368b3 | \([0, -1, 0, -54192, 757152]\) | \(8594236719188066/4858291807551\) | \(9949781621864448\) | \([2]\) | \(32256\) | \(1.7597\) | |
| 4368.j2 | 4368b2 | \([0, -1, 0, -40152, 3104640]\) | \(6991270724335972/14494474449\) | \(14842341835776\) | \([2, 2]\) | \(16128\) | \(1.4131\) | |
| 4368.j3 | 4368b1 | \([0, -1, 0, -40132, 3107872]\) | \(27923315228972368/120393\) | \(30820608\) | \([2]\) | \(8064\) | \(1.0665\) | \(\Gamma_0(N)\)-optimal |
| 4368.j4 | 4368b4 | \([0, -1, 0, -26432, 5244960]\) | \(-997241325462146/5206220835543\) | \(-10662340271192064\) | \([2]\) | \(32256\) | \(1.7597\) |
Rank
sage: E.rank()
The elliptic curves in class 4368.j have rank \(1\).
Complex multiplication
The elliptic curves in class 4368.j do not have complex multiplication.Modular form 4368.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
