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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 275.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
275.b1 | 275b3 | \([0, 1, 1, -195508, -33338481]\) | \(-52893159101157376/11\) | \(-171875\) | \([]\) | \(700\) | \(1.3014\) | |
275.b2 | 275b2 | \([0, 1, 1, -258, -2981]\) | \(-122023936/161051\) | \(-2516421875\) | \([]\) | \(140\) | \(0.49671\) | |
275.b3 | 275b1 | \([0, 1, 1, -8, 19]\) | \(-4096/11\) | \(-171875\) | \([]\) | \(28\) | \(-0.30801\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 275.b have rank \(0\).
Complex multiplication
The elliptic curves in class 275.b do not have complex multiplication.Modular form 275.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.