Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 19845.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19845.k1 | 19845h2 | \([1, -1, 0, -11034, 450813]\) | \(-15590912409/78125\) | \(-744497578125\) | \([]\) | \(27720\) | \(1.1253\) | |
19845.k2 | 19845h1 | \([1, -1, 0, -9, -330]\) | \(-9/5\) | \(-47647845\) | \([]\) | \(3960\) | \(0.15237\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19845.k have rank \(1\).
Complex multiplication
The elliptic curves in class 19845.k do not have complex multiplication.Modular form 19845.2.a.k
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.