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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 152460cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.h2 | 152460cb1 | \([0, 0, 0, -1188, -3267]\) | \(442368/245\) | \(102696446160\) | \([2]\) | \(124416\) | \(0.80338\) | \(\Gamma_0(N)\)-optimal |
152460.h1 | 152460cb2 | \([0, 0, 0, -11583, 476982]\) | \(25625808/175\) | \(1173673670400\) | \([2]\) | \(248832\) | \(1.1500\) |
Rank
sage: E.rank()
The elliptic curves in class 152460cb have rank \(0\).
Complex multiplication
The elliptic curves in class 152460cb do not have complex multiplication.Modular form 152460.2.a.cb
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.