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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 18515.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.n1 | 18515j2 | \([0, 1, 1, -1625, 24679]\) | \(-897625882624/875\) | \(-462875\) | \([]\) | \(6048\) | \(0.38098\) | |
18515.n2 | 18515j1 | \([0, 1, 1, -15, 46]\) | \(-753664/1715\) | \(-907235\) | \([]\) | \(2016\) | \(-0.16832\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18515.n have rank \(1\).
Complex multiplication
The elliptic curves in class 18515.n do not have complex multiplication.Modular form 18515.2.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.