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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53312.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53312.l1 | 53312ch2 | \([0, 1, 0, -87873, 1174207]\) | \(2433138625/1387778\) | \(42800432787488768\) | \([2]\) | \(294912\) | \(1.8811\) | |
| 53312.l2 | 53312ch1 | \([0, 1, 0, -56513, -5166785]\) | \(647214625/3332\) | \(102762143547392\) | \([2]\) | \(147456\) | \(1.5345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53312.l have rank \(2\).
Complex multiplication
The elliptic curves in class 53312.l do not have complex multiplication.Modular form 53312.2.a.l
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 LMFDB 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 LMFDB labels.
