Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 40460.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40460.p1 | 40460c2 | \([0, -1, 0, -191346, -181038979]\) | \(-167558444566341376/2967225943714375\) | \(-13720452763735270000\) | \([]\) | \(894240\) | \(2.3532\) | |
| 40460.p2 | 40460c1 | \([0, -1, 0, 21154, 6513521]\) | \(226392928058624/4103271484375\) | \(-18973527343750000\) | \([]\) | \(298080\) | \(1.8039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40460.p have rank \(0\).
Complex multiplication
The elliptic curves in class 40460.p do not have complex multiplication.Modular form 40460.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
