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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 141570eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.r2 | 141570eb1 | \([1, -1, 0, -530910, 209605050]\) | \(-12814546750201/7261718750\) | \(-9378277165511718750\) | \([]\) | \(3110400\) | \(2.3435\) | \(\Gamma_0(N)\)-optimal |
141570.r3 | 141570eb2 | \([1, -1, 0, 4233465, -2823396075]\) | \(6497225437879799/6424482779000\) | \(-8297013726470605851000\) | \([]\) | \(9331200\) | \(2.8928\) | |
141570.r1 | 141570eb3 | \([1, -1, 0, -101590110, -397941939180]\) | \(-89783052551043953401/1020142489034240\) | \(-1317481348403654704258560\) | \([]\) | \(27993600\) | \(3.4421\) |
Rank
sage: E.rank()
The elliptic curves in class 141570eb have rank \(1\).
Complex multiplication
The elliptic curves in class 141570eb do not have complex multiplication.Modular form 141570.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.