Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 61200.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.l1 | 61200di2 | \([0, 0, 0, -14964075, 22105892250]\) | \(294172502025843/2656250000\) | \(3346110000000000000000\) | \([2]\) | \(4423680\) | \(2.9528\) | |
61200.l2 | 61200di1 | \([0, 0, 0, -276075, 822980250]\) | \(-1847284083/231200000\) | \(-291245414400000000000\) | \([2]\) | \(2211840\) | \(2.6062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61200.l have rank \(0\).
Complex multiplication
The elliptic curves in class 61200.l do not have complex multiplication.Modular form 61200.2.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 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.