Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 390390do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390390.do3 | 390390do1 | \([1, 1, 1, -33532730, -74567623993]\) | \(863913648706111516969/2486234429521920\) | \(12000578720526269153280\) | \([2]\) | \(48168960\) | \(3.1077\) | \(\Gamma_0(N)\)-optimal |
| 390390.do2 | 390390do2 | \([1, 1, 1, -47377210, -7150544185]\) | \(2436531580079063806249/1405478914998681600\) | \(6783978276225871335014400\) | \([2, 2]\) | \(96337920\) | \(3.4543\) | |
| 390390.do1 | 390390do3 | \([1, 1, 1, -505434810, 4357588714695]\) | \(2958414657792917260183849/12401051653985258880\) | \(59857507732920933429313920\) | \([2]\) | \(192675840\) | \(3.8008\) | |
| 390390.do4 | 390390do4 | \([1, 1, 1, 189168710, -56919805753]\) | \(155099895405729262880471/90047655797243760000\) | \(-434642835431038355961840000\) | \([2]\) | \(192675840\) | \(3.8008\) |
Rank
sage: E.rank()
The elliptic curves in class 390390do have rank \(0\).
Complex multiplication
The elliptic curves in class 390390do do not have complex multiplication.Modular form 390390.2.a.do
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
