Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 60112p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60112.h2 | 60112p1 | \([0, 0, 0, -3387947, -2396315750]\) | \(43499078731809/82055753\) | \(8112645733926735872\) | \([2]\) | \(2211840\) | \(2.5184\) | \(\Gamma_0(N)\)-optimal |
| 60112.h1 | 60112p2 | \([0, 0, 0, -54182587, -153510369750]\) | \(177930109857804849/634933\) | \(62774227344904192\) | \([2]\) | \(4423680\) | \(2.8649\) |
Rank
sage: E.rank()
The elliptic curves in class 60112p have rank \(0\).
Complex multiplication
The elliptic curves in class 60112p do not have complex multiplication.Modular form 60112.2.a.p
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.
