Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 146205.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146205.j1 | 146205i2 | \([1, -1, 0, -731634, -241731235]\) | \(-15590912409/78125\) | \(-217032205247578125\) | \([]\) | \(1524096\) | \(2.1739\) | |
146205.j2 | 146205i1 | \([1, -1, 0, -609, 179558]\) | \(-9/5\) | \(-13890061135845\) | \([]\) | \(217728\) | \(1.2009\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146205.j have rank \(0\).
Complex multiplication
The elliptic curves in class 146205.j do not have complex multiplication.Modular form 146205.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.