Show commands:
SageMath
sage: E = EllipticCurve("n1")
sage: E.isogeny_class()
Elliptic curves in class 1470.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1470.n1 | 1470n1 | \([1, 1, 1, -15, -15]\) | \(1092727/540\) | \(185220\) | \([2]\) | \(192\) | \(-0.29613\) | \(\Gamma_0(N)\)-optimal |
1470.n2 | 1470n2 | \([1, 1, 1, 55, -43]\) | \(53582633/36450\) | \(-12502350\) | \([2]\) | \(384\) | \(0.050440\) |
Rank
sage: E.rank()
The elliptic curves in class 1470.n have rank \(0\).
Complex multiplication
The elliptic curves in class 1470.n do not have complex multiplication.Modular form 1470.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.