Show commands:
SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 107184.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107184.cr1 | 107184cv4 | \([0, 1, 0, -190792, -32140108]\) | \(187519537050946633/1186707753\) | \(4860754956288\) | \([2]\) | \(393216\) | \(1.6196\) | |
| 107184.cr2 | 107184cv2 | \([0, 1, 0, -12152, -485100]\) | \(48455467135993/3635004681\) | \(14888979173376\) | \([2, 2]\) | \(196608\) | \(1.2730\) | |
| 107184.cr3 | 107184cv1 | \([0, 1, 0, -2472, 37620]\) | \(408023180713/80247321\) | \(328693026816\) | \([2]\) | \(98304\) | \(0.92645\) | \(\Gamma_0(N)\)-optimal |
| 107184.cr4 | 107184cv3 | \([0, 1, 0, 11608, -2129292]\) | \(42227808999767/504359959257\) | \(-2065858393116672\) | \([2]\) | \(393216\) | \(1.6196\) |
Rank
sage: E.rank()
The elliptic curves in class 107184.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 107184.cr do not have complex multiplication.Modular form 107184.2.a.cr
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.
