Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 60306v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60306.x3 | 60306v1 | \([1, 0, 0, -4243, -8479]\) | \(57066625/32832\) | \(4860314307648\) | \([2]\) | \(142560\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
| 60306.x4 | 60306v2 | \([1, 0, 0, 16917, -63495]\) | \(3616805375/2105352\) | \(-311667654977928\) | \([2]\) | \(285120\) | \(1.4705\) | |
| 60306.x1 | 60306v3 | \([1, 0, 0, -226423, 41450309]\) | \(8671983378625/82308\) | \(12184537951812\) | \([2]\) | \(427680\) | \(1.6732\) | |
| 60306.x2 | 60306v4 | \([1, 0, 0, -221133, 43480611]\) | \(-8078253774625/846825858\) | \(-125360618717217762\) | \([2]\) | \(855360\) | \(2.0198\) |
Rank
sage: E.rank()
The elliptic curves in class 60306v have rank \(0\).
Complex multiplication
The elliptic curves in class 60306v do not have complex multiplication.Modular form 60306.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
