Show commands:
SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 162288eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.bf1 | 162288eu1 | \([0, 0, 0, -19551, 840350]\) | \(109744/23\) | \(173211885713664\) | \([2]\) | \(516096\) | \(1.4470\) | \(\Gamma_0(N)\)-optimal |
| 162288.bf2 | 162288eu2 | \([0, 0, 0, 42189, 5075714]\) | \(275684/529\) | \(-15935493485657088\) | \([2]\) | \(1032192\) | \(1.7935\) |
Rank
sage: E.rank()
The elliptic curves in class 162288eu have rank \(1\).
Complex multiplication
The elliptic curves in class 162288eu do not have complex multiplication.Modular form 162288.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
