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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 7605i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7605.k2 | 7605i1 | \([0, 0, 1, 2652, -27297]\) | \(16742875136/12301875\) | \(-1515603301875\) | \([]\) | \(9216\) | \(1.0255\) | \(\Gamma_0(N)\)-optimal |
7605.k1 | 7605i2 | \([0, 0, 1, -28938, 2338794]\) | \(-21752792449024/6591796875\) | \(-812115966796875\) | \([]\) | \(27648\) | \(1.5748\) |
Rank
sage: E.rank()
The elliptic curves in class 7605i have rank \(0\).
Complex multiplication
The elliptic curves in class 7605i do not have complex multiplication.Modular form 7605.2.a.i
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.