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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 13950bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13950.b2 | 13950bd1 | \([1, -1, 0, -3070692, -2073316784]\) | \(-281115640967896441/468084326400\) | \(-5331773030400000000\) | \([2]\) | \(399360\) | \(2.4892\) | \(\Gamma_0(N)\)-optimal |
13950.b1 | 13950bd2 | \([1, -1, 0, -49150692, -132617956784]\) | \(1152829477932246539641/3188367360\) | \(36317496960000000\) | \([2]\) | \(798720\) | \(2.8357\) |
Rank
sage: E.rank()
The elliptic curves in class 13950bd have rank \(1\).
Complex multiplication
The elliptic curves in class 13950bd do not have complex multiplication.Modular form 13950.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.