Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 71478i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71478.k2 | 71478i1 | \([1, -1, 0, -3213870, -1637465896]\) | \(296518892481/77948684\) | \(965084017345524284076\) | \([]\) | \(3064320\) | \(2.7353\) | \(\Gamma_0(N)\)-optimal |
71478.k1 | 71478i2 | \([1, -1, 0, -2712587460, 54378741733712]\) | \(178286568215258258721/180224\) | \(2231356490150363136\) | \([]\) | \(21450240\) | \(3.7083\) |
Rank
sage: E.rank()
The elliptic curves in class 71478i have rank \(0\).
Complex multiplication
The elliptic curves in class 71478i do not have complex multiplication.Modular form 71478.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.