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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 53816b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53816.c2 | 53816b1 | \([0, 0, 0, -11992319, 68420095970]\) | \(-839504640199248/8415220142959\) | \(-1911945946445173435412224\) | \([2]\) | \(5990400\) | \(3.3414\) | \(\Gamma_0(N)\)-optimal |
| 53816.c1 | 53816b2 | \([0, 0, 0, -335022859, 2353602742038]\) | \(4575904097608151172/14916274366567\) | \(13555966368905375573122048\) | \([2]\) | \(11980800\) | \(3.6880\) |
Rank
sage: E.rank()
The elliptic curves in class 53816b have rank \(1\).
Complex multiplication
The elliptic curves in class 53816b do not have complex multiplication.Modular form 53816.2.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 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.
