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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4410.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.c1 | 4410k2 | \([1, -1, 0, -216540, -38731694]\) | \(-5452947409/250\) | \(-51481114130250\) | \([]\) | \(30240\) | \(1.7066\) | |
4410.c2 | 4410k1 | \([1, -1, 0, -450, -138020]\) | \(-49/40\) | \(-8236978260840\) | \([]\) | \(10080\) | \(1.1573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4410.c have rank \(1\).
Complex multiplication
The elliptic curves in class 4410.c do not have complex multiplication.Modular form 4410.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.