Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 93058f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93058.d2 | 93058f1 | \([1, -1, 0, 181727, -117789315]\) | \(27497120138487/264035631104\) | \(-6373178264231346176\) | \([2]\) | \(1622016\) | \(2.2894\) | \(\Gamma_0(N)\)-optimal |
93058.d1 | 93058f2 | \([1, -1, 0, -2777633, -1648962179]\) | \(98187196835199753/8115872565248\) | \(195897434038880602112\) | \([2]\) | \(3244032\) | \(2.6360\) |
Rank
sage: E.rank()
The elliptic curves in class 93058f have rank \(1\).
Complex multiplication
The elliptic curves in class 93058f do not have complex multiplication.Modular form 93058.2.a.f
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.