Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 33810q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.r1 | 33810q1 | \([1, 1, 0, -1152, -8784]\) | \(1439069689/579600\) | \(68189360400\) | \([2]\) | \(36864\) | \(0.77676\) | \(\Gamma_0(N)\)-optimal |
33810.r2 | 33810q2 | \([1, 1, 0, 3748, -58764]\) | \(49471280711/41992020\) | \(-4940319160980\) | \([2]\) | \(73728\) | \(1.1233\) |
Rank
sage: E.rank()
The elliptic curves in class 33810q have rank \(1\).
Complex multiplication
The elliptic curves in class 33810q do not have complex multiplication.Modular form 33810.2.a.q
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.