Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 29120l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29120.bg1 | 29120l1 | \([0, 0, 0, -54092, 4842224]\) | \(267080942160036/1990625\) | \(130457600000\) | \([2]\) | \(71680\) | \(1.3088\) | \(\Gamma_0(N)\)-optimal |
29120.bg2 | 29120l2 | \([0, 0, 0, -52972, 5052336]\) | \(-125415986034978/11552734375\) | \(-1514240000000000\) | \([2]\) | \(143360\) | \(1.6554\) |
Rank
sage: E.rank()
The elliptic curves in class 29120l have rank \(2\).
Complex multiplication
The elliptic curves in class 29120l do not have complex multiplication.Modular form 29120.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.