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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 47915.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47915.b1 | 47915c3 | \([0, 1, 1, -179795, -30756119]\) | \(-250523582464/13671875\) | \(-35078290748046875\) | \([]\) | \(311040\) | \(1.9329\) | |
47915.b2 | 47915c1 | \([0, 1, 1, -1825, 32691]\) | \(-262144/35\) | \(-89800424315\) | \([]\) | \(34560\) | \(0.83431\) | \(\Gamma_0(N)\)-optimal |
47915.b3 | 47915c2 | \([0, 1, 1, 11865, -80936]\) | \(71991296/42875\) | \(-110005519785875\) | \([]\) | \(103680\) | \(1.3836\) |
Rank
sage: E.rank()
The elliptic curves in class 47915.b have rank \(1\).
Complex multiplication
The elliptic curves in class 47915.b do not have complex multiplication.Modular form 47915.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.