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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4598i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4598.h1 | 4598i1 | \([1, 0, 1, -971, 12340]\) | \(-471625/38\) | \(-8145637478\) | \([3]\) | \(3168\) | \(0.64815\) | \(\Gamma_0(N)\)-optimal |
4598.h2 | 4598i2 | \([1, 0, 1, 5684, 4354]\) | \(94766375/54872\) | \(-11762300518232\) | \([]\) | \(9504\) | \(1.1975\) |
Rank
sage: E.rank()
The elliptic curves in class 4598i have rank \(1\).
Complex multiplication
The elliptic curves in class 4598i do not have complex multiplication.Modular form 4598.2.a.i
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.