Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 176400.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.e1 | 176400dl2 | \([0, 0, 0, -117075, 16735250]\) | \(-77626969/8000\) | \(-18289152000000000\) | \([]\) | \(1244160\) | \(1.8599\) | |
176400.e2 | 176400dl1 | \([0, 0, 0, 8925, -22750]\) | \(34391/20\) | \(-45722880000000\) | \([]\) | \(414720\) | \(1.3106\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.e have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.e do not have complex multiplication.Modular form 176400.2.a.e
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.