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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 16562m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.f2 | 16562m1 | \([1, 1, 0, 24671, 951371]\) | \(17303/14\) | \(-1343578650329006\) | \([]\) | \(89856\) | \(1.5907\) | \(\Gamma_0(N)\)-optimal |
16562.f1 | 16562m2 | \([1, 1, 0, -513594, 143591596]\) | \(-156116857/2744\) | \(-263341415464485176\) | \([]\) | \(269568\) | \(2.1400\) |
Rank
sage: E.rank()
The elliptic curves in class 16562m have rank \(0\).
Complex multiplication
The elliptic curves in class 16562m do not have complex multiplication.Modular form 16562.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.