Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 75712.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.q1 | 75712cg1 | \([0, 1, 0, -43489, -3505761]\) | \(-1214950633/196\) | \(-1467470577664\) | \([]\) | \(276480\) | \(1.3440\) | \(\Gamma_0(N)\)-optimal |
75712.q2 | 75712cg2 | \([0, 1, 0, 10591, -11412257]\) | \(17546087/7529536\) | \(-56374349711540224\) | \([]\) | \(829440\) | \(1.8933\) |
Rank
sage: E.rank()
The elliptic curves in class 75712.q have rank \(0\).
Complex multiplication
The elliptic curves in class 75712.q do not have complex multiplication.Modular form 75712.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.