Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 44880.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.m1 | 44880bk1 | \([0, -1, 0, -29941, -2041859]\) | \(-724731558068224/24623341875\) | \(-100857208320000\) | \([]\) | \(124416\) | \(1.4608\) | \(\Gamma_0(N)\)-optimal |
44880.m2 | 44880bk2 | \([0, -1, 0, 141419, -7285475]\) | \(76363175346569216/49717529296875\) | \(-203643000000000000\) | \([]\) | \(373248\) | \(2.0101\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.m have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.m do not have complex multiplication.Modular form 44880.2.a.m
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.