Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1950.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.o1 | 1950n4 | \([1, 1, 1, -21814438, -39224901469]\) | \(73474353581350183614361/576510977802240\) | \(9007984028160000000\) | \([2]\) | \(103680\) | \(2.8101\) | |
1950.o2 | 1950n3 | \([1, 1, 1, -1334438, -640581469]\) | \(-16818951115904497561/1592332281446400\) | \(-24880191897600000000\) | \([2]\) | \(51840\) | \(2.4635\) | |
1950.o3 | 1950n2 | \([1, 1, 1, -400063, 3499781]\) | \(453198971846635561/261896250564000\) | \(4092128915062500000\) | \([2]\) | \(34560\) | \(2.2608\) | |
1950.o4 | 1950n1 | \([1, 1, 1, 99937, 499781]\) | \(7064514799444439/4094064000000\) | \(-63969750000000000\) | \([2]\) | \(17280\) | \(1.9142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1950.o have rank \(0\).
Complex multiplication
The elliptic curves in class 1950.o do not have complex multiplication.Modular form 1950.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.