Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 155526.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.c1 | 155526ct2 | \([1, 1, 0, -635604, 131961936]\) | \(862551551257/269746176\) | \(8880857077372944384\) | \([]\) | \(3483648\) | \(2.3401\) | |
155526.c2 | 155526ct1 | \([1, 1, 0, -246789, -47281779]\) | \(50489872297/12096\) | \(398236775033664\) | \([]\) | \(1161216\) | \(1.7908\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.c have rank \(1\).
Complex multiplication
The elliptic curves in class 155526.c do not have complex multiplication.Modular form 155526.2.a.c
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.