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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 14450.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.c1 | 14450k2 | \([1, 1, 0, -4655, 120325]\) | \(-18170704189/32\) | \(-19652000\) | \([]\) | \(8960\) | \(0.65853\) | |
14450.c2 | 14450k1 | \([1, 1, 0, 20, 50]\) | \(1331/2\) | \(-1228250\) | \([]\) | \(1792\) | \(-0.14619\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14450.c have rank \(2\).
Complex multiplication
The elliptic curves in class 14450.c do not have complex multiplication.Modular form 14450.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.