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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 122694.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.bd1 | 122694bm1 | \([1, 0, 1, -7505, -438748]\) | \(-156116857/186624\) | \(-55874070210816\) | \([]\) | \(414720\) | \(1.3317\) | \(\Gamma_0(N)\)-optimal |
122694.bd2 | 122694bm2 | \([1, 0, 1, 63280, 8197022]\) | \(93603087383/150994944\) | \(-45206951423901696\) | \([]\) | \(1244160\) | \(1.8810\) |
Rank
sage: E.rank()
The elliptic curves in class 122694.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 122694.bd do not have complex multiplication.Modular form 122694.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.