Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 45177m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45177.l2 | 45177m1 | \([1, 0, 1, -10904114, 20120476439]\) | \(-1103263596037/707347971\) | \(-91928172951677671738767\) | \([2]\) | \(6521472\) | \(3.1076\) | \(\Gamma_0(N)\)-optimal |
45177.l1 | 45177m2 | \([1, 0, 1, -195534299, 1052203210589]\) | \(6361756446348757/1291467969\) | \(167841424140854569388613\) | \([2]\) | \(13042944\) | \(3.4542\) |
Rank
sage: E.rank()
The elliptic curves in class 45177m have rank \(0\).
Complex multiplication
The elliptic curves in class 45177m do not have complex multiplication.Modular form 45177.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.