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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2310b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2310.b3 | 2310b1 | \([1, 1, 0, -198418, -34016972]\) | \(863913648706111516969/2486234429521920\) | \(2486234429521920\) | \([2]\) | \(25088\) | \(1.8252\) | \(\Gamma_0(N)\)-optimal |
| 2310.b2 | 2310b2 | \([1, 1, 0, -280338, -3362508]\) | \(2436531580079063806249/1405478914998681600\) | \(1405478914998681600\) | \([2, 2]\) | \(50176\) | \(2.1718\) | |
| 2310.b1 | 2310b3 | \([1, 1, 0, -2990738, 1982276532]\) | \(2958414657792917260183849/12401051653985258880\) | \(12401051653985258880\) | \([2]\) | \(100352\) | \(2.5184\) | |
| 2310.b4 | 2310b4 | \([1, 1, 0, 1119342, -25477452]\) | \(155099895405729262880471/90047655797243760000\) | \(-90047655797243760000\) | \([2]\) | \(100352\) | \(2.5184\) |
Rank
sage: E.rank()
The elliptic curves in class 2310b have rank \(0\).
Complex multiplication
The elliptic curves in class 2310b do not have complex multiplication.Modular form 2310.2.a.b
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.
