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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28980j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28980.h1 | 28980j1 | \([0, 0, 0, -90912, -10550059]\) | \(7124261256822784/475453125\) | \(5545685250000\) | \([2]\) | \(138240\) | \(1.5009\) | \(\Gamma_0(N)\)-optimal |
28980.h2 | 28980j2 | \([0, 0, 0, -85287, -11912434]\) | \(-367624742361424/115740505125\) | \(-21599956028448000\) | \([2]\) | \(276480\) | \(1.8475\) |
Rank
sage: E.rank()
The elliptic curves in class 28980j have rank \(0\).
Complex multiplication
The elliptic curves in class 28980j do not have complex multiplication.Modular form 28980.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.