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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11830c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11830.l2 | 11830c1 | \([1, 0, 1, -4, -674]\) | \(-169/6860\) | \(-195928460\) | \([3]\) | \(4608\) | \(0.27000\) | \(\Gamma_0(N)\)-optimal |
11830.l1 | 11830c2 | \([1, 0, 1, -5919, -175758]\) | \(-802767616729/56000\) | \(-1599416000\) | \([]\) | \(13824\) | \(0.81930\) |
Rank
sage: E.rank()
The elliptic curves in class 11830c have rank \(0\).
Complex multiplication
The elliptic curves in class 11830c do not have complex multiplication.Modular form 11830.2.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 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.