Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 390.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
390.b1 | 390f2 | \([1, 1, 0, -852, -9936]\) | \(68523370149961/243360\) | \(243360\) | \([2]\) | \(160\) | \(0.25184\) | |
390.b2 | 390f1 | \([1, 1, 0, -52, -176]\) | \(-16022066761/998400\) | \(-998400\) | \([2]\) | \(80\) | \(-0.094738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 390.b have rank \(0\).
Complex multiplication
The elliptic curves in class 390.b do not have complex multiplication.Modular form 390.2.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 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.