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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11550.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.c1 | 11550b1 | \([1, 1, 0, -240950, 45436500]\) | \(-158419003440625/52157952\) | \(-509355000000000\) | \([]\) | \(116640\) | \(1.7954\) | \(\Gamma_0(N)\)-optimal |
11550.c2 | 11550b2 | \([1, 1, 0, 134050, 169711500]\) | \(27278410559375/1289055622008\) | \(-12588433808671875000\) | \([]\) | \(349920\) | \(2.3447\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.c have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.c do not have complex multiplication.Modular form 11550.2.a.c
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.