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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 152460.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.n1 | 152460be1 | \([0, 0, 0, -2445168, 3044705092]\) | \(-4890195460096/9282994875\) | \(-3069104777588136672000\) | \([]\) | \(7464960\) | \(2.8128\) | \(\Gamma_0(N)\)-optimal |
152460.n2 | 152460be2 | \([0, 0, 0, 21077232, -64513979948]\) | \(3132137615458304/7250937873795\) | \(-2397274626359092984922880\) | \([]\) | \(22394880\) | \(3.3621\) |
Rank
sage: E.rank()
The elliptic curves in class 152460.n have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.n do not have complex multiplication.Modular form 152460.2.a.n
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.