Show commands:
SageMath
E = EllipticCurve("ti1")
E.isogeny_class()
Elliptic curves in class 176400.ti
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.ti1 | 176400dk2 | \([0, 0, 0, -25317901875, -1550563948228750]\) | \(266916252066900625/162\) | \(1089298349596800000000\) | \([]\) | \(174182400\) | \(4.2593\) | |
176400.ti2 | 176400dk1 | \([0, 0, 0, -313201875, -2117895088750]\) | \(505318200625/4251528\) | \(28587545886818419200000000\) | \([]\) | \(58060800\) | \(3.7100\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.ti have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.ti do not have complex multiplication.Modular form 176400.2.a.ti
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.