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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 18837j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18837.l2 | 18837j1 | \([1, -1, 0, 153, 688]\) | \(541343375/625807\) | \(-456213303\) | \([2]\) | \(5760\) | \(0.34788\) | \(\Gamma_0(N)\)-optimal |
18837.l1 | 18837j2 | \([1, -1, 0, -882, 7105]\) | \(104154702625/32188247\) | \(23465232063\) | \([2]\) | \(11520\) | \(0.69446\) |
Rank
sage: E.rank()
The elliptic curves in class 18837j have rank \(0\).
Complex multiplication
The elliptic curves in class 18837j do not have complex multiplication.Modular form 18837.2.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.