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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 250200c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250200.c1 | 250200c1 | \([0, 0, 0, -280875, -57294250]\) | \(210094874500/3753\) | \(43774992000000\) | \([2]\) | \(1548288\) | \(1.7445\) | \(\Gamma_0(N)\)-optimal |
250200.c2 | 250200c2 | \([0, 0, 0, -271875, -61137250]\) | \(-95269531250/14085009\) | \(-328575089952000000\) | \([2]\) | \(3096576\) | \(2.0911\) |
Rank
sage: E.rank()
The elliptic curves in class 250200c have rank \(0\).
Complex multiplication
The elliptic curves in class 250200c do not have complex multiplication.Modular form 250200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.