Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 316239o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
316239.o2 | 316239o1 | \([1, 1, 0, 42411, -2349360]\) | \(3288008303/2846151\) | \(-7302444784701759\) | \([2]\) | \(2101248\) | \(1.7315\) | \(\Gamma_0(N)\)-optimal |
316239.o1 | 316239o2 | \([1, 1, 0, -210854, -21040317]\) | \(404075127457/159922917\) | \(410318451551215053\) | \([2]\) | \(4202496\) | \(2.0780\) |
Rank
sage: E.rank()
The elliptic curves in class 316239o have rank \(0\).
Complex multiplication
The elliptic curves in class 316239o do not have complex multiplication.Modular form 316239.2.a.o
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.