Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 214774.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214774.a1 | 214774g2 | \([1, 0, 1, -286465, 54175536]\) | \(17561807821657/1590616244\) | \(235468289738380916\) | \([2]\) | \(2703360\) | \(2.0728\) | |
214774.a2 | 214774g1 | \([1, 0, 1, 20355, 3979784]\) | \(6300872423/49827568\) | \(-7376268325587952\) | \([2]\) | \(1351680\) | \(1.7262\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214774.a have rank \(0\).
Complex multiplication
The elliptic curves in class 214774.a do not have complex multiplication.Modular form 214774.2.a.a
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.