Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 148225.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.ba1 | 148225y2 | \([1, 0, 0, -629451138, 6078373746017]\) | \(-162677523113838677\) | \(-169543923828125\) | \([]\) | \(12787200\) | \(3.2742\) | |
148225.ba2 | 148225y1 | \([1, 0, 0, -24263, -1585858]\) | \(-9317\) | \(-169543923828125\) | \([]\) | \(345600\) | \(1.4687\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148225.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 148225.ba do not have complex multiplication.Modular form 148225.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.