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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 274890b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.b1 | 274890b1 | \([1, 1, 0, -5023, -141623]\) | \(-119168121961/2524500\) | \(-297004900500\) | \([]\) | \(544320\) | \(0.99184\) | \(\Gamma_0(N)\)-optimal |
274890.b2 | 274890b2 | \([1, 1, 0, 20702, -620108]\) | \(8339492177639/6277634880\) | \(-738557465997120\) | \([]\) | \(1632960\) | \(1.5411\) |
Rank
sage: E.rank()
The elliptic curves in class 274890b have rank \(1\).
Complex multiplication
The elliptic curves in class 274890b do not have complex multiplication.Modular form 274890.2.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.