Show commands:
SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 35280.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.fi1 | 35280fa2 | \([0, 0, 0, -70707, -7237006]\) | \(-5452947409/250\) | \(-1792336896000\) | \([]\) | \(103680\) | \(1.4268\) | |
35280.fi2 | 35280fa1 | \([0, 0, 0, -147, -25774]\) | \(-49/40\) | \(-286773903360\) | \([]\) | \(34560\) | \(0.87754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.fi have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.fi do not have complex multiplication.Modular form 35280.2.a.fi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.