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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 333200dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333200.dd1 | 333200dd1 | \([0, 0, 0, -34300, 2443875]\) | \(151732224/85\) | \(2500041250000\) | \([2]\) | \(663552\) | \(1.3261\) | \(\Gamma_0(N)\)-optimal |
| 333200.dd2 | 333200dd2 | \([0, 0, 0, -28175, 3344250]\) | \(-5256144/7225\) | \(-3400056100000000\) | \([2]\) | \(1327104\) | \(1.6727\) |
Rank
sage: E.rank()
The elliptic curves in class 333200dd have rank \(0\).
Complex multiplication
The elliptic curves in class 333200dd do not have complex multiplication.Modular form 333200.2.a.dd
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.
