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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 17136.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17136.m1 | 17136t2 | \([0, 0, 0, -153711, 21955050]\) | \(79708988544624/4802079233\) | \(24196947339043584\) | \([2]\) | \(126720\) | \(1.8963\) | |
17136.m2 | 17136t1 | \([0, 0, 0, -151416, 22677975]\) | \(1219067475001344/4857223\) | \(1529675524944\) | \([2]\) | \(63360\) | \(1.5497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17136.m have rank \(1\).
Complex multiplication
The elliptic curves in class 17136.m do not have complex multiplication.Modular form 17136.2.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.