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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 170352.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170352.m1 | 170352l2 | \([0, 0, 0, -1509339, -724478326]\) | \(-156116857/2744\) | \(-6683722370052489216\) | \([]\) | \(4043520\) | \(2.4095\) | |
170352.m2 | 170352l1 | \([0, 0, 0, 72501, -4741126]\) | \(17303/14\) | \(-34100624337002496\) | \([]\) | \(1347840\) | \(1.8602\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 170352.m have rank \(1\).
Complex multiplication
The elliptic curves in class 170352.m do not have complex multiplication.Modular form 170352.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.