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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 230115c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230115.c1 | 230115c1 | \([1, 1, 1, -21171, -1187232]\) | \(7088952961/50025\) | \(7405495347225\) | \([2]\) | \(1081344\) | \(1.3021\) | \(\Gamma_0(N)\)-optimal |
230115.c2 | 230115c2 | \([1, 1, 1, -7946, -2636692]\) | \(-374805361/20020005\) | \(-2963679237959445\) | \([2]\) | \(2162688\) | \(1.6487\) |
Rank
sage: E.rank()
The elliptic curves in class 230115c have rank \(1\).
Complex multiplication
The elliptic curves in class 230115c do not have complex multiplication.Modular form 230115.2.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.