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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 23520r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.bh3 | 23520r1 | \([0, 1, 0, -257266, 50128784]\) | \(250094631024064/62015625\) | \(466948881000000\) | \([2, 2]\) | \(147456\) | \(1.8023\) | \(\Gamma_0(N)\)-optimal |
| 23520.bh4 | 23520r2 | \([0, 1, 0, -226641, 62544159]\) | \(-2671731885376/1969120125\) | \(-948899895648768000\) | \([2]\) | \(294912\) | \(2.1489\) | |
| 23520.bh2 | 23520r3 | \([0, 1, 0, -288136, 37311560]\) | \(43919722445768/15380859375\) | \(926485875000000000\) | \([2]\) | \(294912\) | \(2.1489\) | |
| 23520.bh1 | 23520r4 | \([0, 1, 0, -4116016, 3212760284]\) | \(128025588102048008/7875\) | \(474360768000\) | \([2]\) | \(294912\) | \(2.1489\) |
Rank
sage: E.rank()
The elliptic curves in class 23520r have rank \(1\).
Complex multiplication
The elliptic curves in class 23520r do not have complex multiplication.Modular form 23520.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
