Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 23120o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.t2 | 23120o1 | \([0, 0, 0, -323, 578]\) | \(185193/100\) | \(2012364800\) | \([2]\) | \(9216\) | \(0.47626\) | \(\Gamma_0(N)\)-optimal |
23120.t1 | 23120o2 | \([0, 0, 0, -3043, -64158]\) | \(154854153/1250\) | \(25154560000\) | \([2]\) | \(18432\) | \(0.82283\) |
Rank
sage: E.rank()
The elliptic curves in class 23120o have rank \(2\).
Complex multiplication
The elliptic curves in class 23120o do not have complex multiplication.Modular form 23120.2.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.