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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 90354c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.b2 | 90354c1 | \([1, 1, 0, 1151301, 406350531]\) | \(1298596571/1299078\) | \(-168830437009509039006\) | \([]\) | \(3729600\) | \(2.5682\) | \(\Gamma_0(N)\)-optimal |
90354.b1 | 90354c2 | \([1, 1, 0, -215390274, 1216626466644]\) | \(-8503279704467029/46382688\) | \(-6027974828852240426976\) | \([]\) | \(18648000\) | \(3.3729\) |
Rank
sage: E.rank()
The elliptic curves in class 90354c have rank \(0\).
Complex multiplication
The elliptic curves in class 90354c do not have complex multiplication.Modular form 90354.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.