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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 381150eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.eb1 | 381150eb1 | \([1, -1, 0, -15500667, -23434863259]\) | \(551105805571803/1376829440\) | \(1029011065125120000000\) | \([2]\) | \(34406400\) | \(2.9093\) | \(\Gamma_0(N)\)-optimal |
381150.eb2 | 381150eb2 | \([1, -1, 0, -9692667, -41213151259]\) | \(-134745327251163/903920796800\) | \(-675569881701480150000000\) | \([2]\) | \(68812800\) | \(3.2558\) |
Rank
sage: E.rank()
The elliptic curves in class 381150eb have rank \(0\).
Complex multiplication
The elliptic curves in class 381150eb do not have complex multiplication.Modular form 381150.2.a.eb
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.