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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 407330.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
407330.c1 | 407330c1 | \([1, 0, 1, -170614, 17833236]\) | \(3710197529641/1217562500\) | \(180242947100562500\) | \([2]\) | \(5271552\) | \(2.0141\) | \(\Gamma_0(N)\)-optimal |
407330.c2 | 407330c2 | \([1, 0, 1, 490636, 122575236]\) | \(88234047450359/94877340250\) | \(-14045251409864232250\) | \([2]\) | \(10543104\) | \(2.3607\) |
Rank
sage: E.rank()
The elliptic curves in class 407330.c have rank \(0\).
Complex multiplication
The elliptic curves in class 407330.c do not have complex multiplication.Modular form 407330.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.