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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 53900b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53900.l2 | 53900b1 | \([0, -1, 0, 151492, 17045512]\) | \(16674224/15125\) | \(-348770460500000000\) | \([]\) | \(580608\) | \(2.0534\) | \(\Gamma_0(N)\)-optimal |
53900.l1 | 53900b2 | \([0, -1, 0, -1563508, -1018814488]\) | \(-18330740176/8857805\) | \(-204253932487220000000\) | \([]\) | \(1741824\) | \(2.6027\) |
Rank
sage: E.rank()
The elliptic curves in class 53900b have rank \(0\).
Complex multiplication
The elliptic curves in class 53900b do not have complex multiplication.Modular form 53900.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.