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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 53361.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.m1 | 53361n2 | \([1, -1, 1, -890462, -321419150]\) | \(19034163/121\) | \(496387702582306227\) | \([2]\) | \(1036800\) | \(2.2325\) | |
53361.m2 | 53361n1 | \([1, -1, 1, -90047, 1948510]\) | \(19683/11\) | \(45126154780209657\) | \([2]\) | \(518400\) | \(1.8859\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53361.m have rank \(1\).
Complex multiplication
The elliptic curves in class 53361.m do not have complex multiplication.Modular form 53361.2.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 LMFDB 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 LMFDB labels.