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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 380926c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.c2 | 380926c1 | \([1, 0, 1, -33297, -2152720]\) | \(7189057/644\) | \(365707798314404\) | \([2]\) | \(2488320\) | \(1.5342\) | \(\Gamma_0(N)\)-optimal |
380926.c1 | 380926c2 | \([1, 0, 1, -116107, 12786204]\) | \(304821217/51842\) | \(29439477764309522\) | \([2]\) | \(4976640\) | \(1.8807\) |
Rank
sage: E.rank()
The elliptic curves in class 380926c have rank \(1\).
Complex multiplication
The elliptic curves in class 380926c do not have complex multiplication.Modular form 380926.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.